There’s little difference, as these two citations from the OED, both from the 1980s, show:
She and Roy would nibble on each other.
Encircling her slim waist with a fond arm, the husband of a fortnight
nibbles her throat.
Neither describes an act of cannibalism.
In leaves no step had trodden black.
This line refers to leaves that have been stepped on to the point where they are black instead of the color they were when they fell off the tree.
The word "tread" means (one of its meanings) "to step on." So you can tread on the leaves as you walk along. If you have stepped on the leaf, we can say you have trodden on it.
So the speaker is saying (at this point) that that road has not been walked on. The leaves have not been stepped on so they have not turned black from being crushed or ground into the dirt or anything.
And that has made all the difference.
In this case, the narrator, reflects that, of the two paths he could have taken in life, he chose to follow "the one less traveled by," and he believes "that has made all the difference." Basically, the narrator reached a point in his life when he was faced with decision to either conform to society and live a "normal" life, or to live his life in way that embraces individuality or an less conventional existence than the first path.
The road that fewer people had taken ("was more grassy and wanted wear") was more inviting to the narrator, so he made the choice to follow the path that fewer people had taken. The narrator believes that chosing to follow the norm would have been the wrong decision.
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Best Answer
A predicate needs its argument to complete the meaning. An object is one as such (direct argument); the preposition phrase is another (oblique argument) but very much essential to the meaning of the sentence. The preposition is the argument marker.
Not going into pedantic details, we can say this much that in both sets of examples
WAYis used all along as a noun. We don't find fault with the first set of examples —IN ANOTHER WAY— is anAdverb Prepositional Phrase(preposition in the beginning, its object at the end and a modifier in between; in - another - way). It fulfills oblique argument in the first set of three.What about the rest?
WAYis not an adverb here.WAYor for that matterANOTHER WAYis anadverbial objective(they create an object like illusion though not acted upon) oradverbial nouni.e., nouns used as adverb:Mornings and nightsoccupy the position earmarked for an object. But a word of caution: adverbial nouns modify verbs and adjectives and they are not used to describe manners.However, in the first two of the remaining set of three
another wayfunctions as adverbial objective – localising the functionality of the verbs. But in the last sentence we wantanother wayto function as an adverbial objective assigning the role to describe manners which is contrary to its nature. The last sentence flouts basic rules of semantics and is wrong as such:In this example sentence the participle object phrase
building roadscan be classified as an object of another objectroadsusurping (leaving no room for) adverbial objective (yet another noun —another way). So we have:Building (noun equivalent participle)
Roads (noun)
Another way (noun)
Without a relationship word (preposition)
another waycan not be knit in the sentence coherently or logically. However, I have a sort of inner prompting that says that ifroadsbe replaced by any pronoun (it/this/one) thananother waymay be induced in the sentence without a preposition but the rule underlying is beyond my knowledge.