When decline is used as a transitive verb, it means "to refuse" or "to say no to": We are declining your loan application. - I regret that I must decline your invitation. Declining a customer would be a bad business move; declining your customer base is simply ungrammatical. Probably bad business too.
When a sentient actor (a person, a corporation, an intelligent animal) is the subject of decline in an apparently intransitive sense, there is generally an implied object; I would call this a "virtually transitive" use: I offered him a job, but he declined (the job). - We offered the chimp a banana, but she declined (the banana).
When a non-sentient noun is used as the subject of decline, it means that that thing/resource/quality is becoming less, or less powerful: The puma population has been declining for the past few years. - Hari Seldon says that the Empire is declining.
When a thing is declining, or a person's health or power is declining, we can say that that thing or person is in decline. As soon as his team started losing, he went into a decline. - This country's been in decline ever since they raised the drinking age.
When decrease is used as a transitive verb, it means "to reduce the amount of": I'll have to decrease my donut intake, or else my chair will break.
Sentient actors don't decrease intransitively; you can't say He decreased.
When a non-sentient noun is used as the subject of decrease, it means that that thing/resource/quality is becoming less: The puma population has been decreasing for the past few years. but NOT Hari Seldon says that the Empire is decreasing.
A crucial difference between decline and decrease in this last case is that decline can be used to indicate a loss of power, influence, significance, etc., whereas decrease can only be used for a reduction in quantity. Thus you can say both The population is decreasing and The population is declining, but while you can say The Empire is declining, you cannot say The Empire is decreasing, since there's still only one Empire.
Of your four sentences, only the first is entirely acceptable as it stands. The rest are little ambiguous; they may represent acceptable elliptical constructions; but they cannot be used to represent the same meaning as the first.
I’ll strip out the specific words and use abstract X and Y for the nouns and abstract A for the positive adjective, with A-er as its comparative grade. A-ness is the quality expressed by A.
- X is A-er than Y.
- ?X is A-er rather than Y.
- ?X is A-er to Y.
- ?X is A-er above Y.
Sentence 1 states that X has more A-ness than Y has.
Rather than means instead of or and not or in preference to, and Sentence 2 may be parsed a couple of different ways. Most simply, it claims that X, and not Y, has more A-ness than something else—call it Z. Under this parsing the sentence is an elliptical form of
2a. X, rather than Y, is A-er [than Z]. (Note that we have to move the rather than phrase; if we left it at the end it would mean It is Y, rather than Z, which X is A-er than.)
However, it is possible that X and Y are being compared to each other, as in Sentence 1. In that case, the sentence would be parsed as an elliptical form of
2b. X is A-er [than Y], rather than Y [being A-er than X].
In both cases, however, it is the construction A-er than which performs the comparison; rather than heads an adverbial phrase which modifies the core statement.
The rather than construction can also be used to compare two verbal phrases instead of two nouns, and in this case the construction may be split:
2c. I would rather do X than [do] Y. eg, I would rather eat ice cream than broccoli.
2d. I would rather VX than VY. eg, I would rather eat ice cream than be boiled in oil.
In Sentence 3, to is a preposition which plays no part in a comparison. It may, however, be a component of a gradable “phrasal adjective” (that’s a term I just made up) like close to. If that phrasal adjective exists, the sentence could be parsed in two ways, as two different ellipses:
3a. X is A-er to Y [than X is to Z]. eg New York is closer to Washington than Chicago.
3b. X is A-er to Y [than Z is to Y]. eg New York is closer to Washington than Boston.
(But the phrasal adjective better to is not current in English, so as it stands your own sentence is not acceptable.)
The to might also be used with the -ed participle of a verb which performs a comparison; to then would be either the head of a prepositional phrase modifying the verb or a prepositional component of a phrasal main verb—it’s often hard to draw the line between these. In any case, the participle would be in positive form, not comparative, since the comparative sense would be expressed lexically:
3c. X is V-d to Y. eg New York is preferred to Washington.
In Sentence 4, above works the same way; I can’t offhand think of a phrasal adjective with above, but here’s a use with a participle:
4a. X is V-d above Y. eg New York is ranked above Washington.
But a comparison employing a comparative-grade adjective almost always implies the construction with than in your Sentence 1; so Sentences 3 and 4 are unacceptable with better or with any other A-er form which does not form a phrasal adjective with the preposition.
Best Answer
The earliest use of the word title is for an inscription placed by an object (or person, it comes from the Latin titulus and first appears in regards to the inscription "Iesus Nazarenus, Rex Iudaeorum" placed above Christ during the Crucifixion), or a placard in a theatre giving the name of the play currently being shown.
From this another early sense is of the inscription at the top of a chapter or section, or on the cover or title-page of a book.
Now, the title in this sense would of course also be used as the name of the book should one wish to refer to it, or at least we might create a name for it by abbreviating the title (e.g. the book with the title The Life and Strange Surprizing Adventures of Robinson Crusoe, Of York, Mariner: Who lived Eight and Twenty Years, all alone in an un-inhabited Island on the Coast of America, near the Mouth of the Great River of Oroonoque; Having been cast on Shore by Shipwreck, wherein all the Men perished but himself. With An Account how he was at last as strangely deliver'd by Pyrates is best-known by the name "Robinson Crusoe").
Increasingly, as short titles became more common, the title and name of a book is almost always the same.
There are some exceptions, e.g. "K&R" and "The White Bible" or both names for the book with the title The C Programming Language (which is also a name for it), "The Camel Book" is a name for Programming Perl, and so on. Among Star-Wars fans, "Empire" is recognised as a name for the film that has been released under the titles The Empire Strikes Back and Star Wars Episode V: The Empire Strikes Back. Some songs are known by names other than their titles, particularly from choral lines.
As such, even in those cases you mention as more often having titles than names, the two are overlapping but not identical; such works may have more than one titles, and then my have yet further names again.
But for all that, it's still the case that the title will almost always be a name, and often recognised as the "real" name.
"File name" is a slightly more complicated case. The concept goes back to the Compatible Time-Sharing System and "file title" could have arguably have made just as much (metaphorical) sense. In retrospect the jargon chosen works well with the distinction I describe above though, since hierarchical file systems, multi-host systems and aliasing all mean that there is more to the name(s) of a file from a given position in the system than just the title given to it.
And so, a title is what someone has associated with something through printing it on or near them, or otherwise formally asserting is the name, while name is wider again and refers to anything it has been formally or informally referred to. By extension, it also applies to where this would often be done even if it never was (a picture with no plaque, a song for which the music or lyrics have never been printed).
In those cases where the name is also the title (hence films, books, songs, chapters, etc. with the caveat about other names already mentioned) we favour the more specific title over the more general name, to the point of this being more idiomatic.
(Title in the sense of e.g. an honorific or an hereditary title is another case again).