In grammar, the idea of modality is to express subjective attitudes and opinions of the speaker about a possibility, probability, necessity, obligation, permission, ability, desire, and contingency.
All these categories can be ranked by the degree from high to low, where must refers to the former and would — to the latter.
In other words, must asserts what we conclude to be the most likely interpretation of a situation or events, and would — a less likely one.
Cut to the chase, compared with would, must expresses a higher degree of probability and means "I'm sure", "I'm most certain", "most probably" whereas would means "I suppose/assume", "probably", "maybe", "I should think".
To refer to the past, we use would with the perfect infinitive:
A: I met a most beautiful girl at John's party yesterday.
B: Ah, yes! That would have been his cousine Ann.
P.S. Should you want to have modal verbs listed by their modality strength approximately, here you are:
High modality: must, ought to, shall, has to;
Medium modality: will, should, can, need to;
Low modality: may, might, could, would.
You should bear in mind that the idea of modality can also be expressed through nouns, adjectives and adverbs:
Modal nouns: possibility, probability, certainty, obligation,
necessity, requirement;
Modal adjectives: possible, probable, obligatory, necessary,
required, determined, likely, certain;
Modal adverbs: possibly, probably, maybe, perhaps, sometimes, always,
never, certainly, definitely.
The correct way to use must is this, which is equivalent to saying had to stop:
During a tour of the factory, health and safety inspectors declared that the company must stop production until a series of tests were carried out.
Must have stopped would refer to a time further in the past when production actually or was believed to have actually stopped. In the sentence above, the company received a declaration saying they must do X, but we don't know if the company actually did it yet (if penalties are severe that could be strongly implied though)
For example:
The company must have stopped production until a series of tests were carried out, because of a declaration by health and safety inspectors. (we believe the company actually did stop production and are trying to figure out why)
Best Answer
When you paraphrase you hope to give a sentence with similar meaning. There are very few pairs of sentences with exactly the same meaning, register, tone and nuance.
"Must have" is used to indicate deductions or conclusions from evidence.
It implies that you did not directly observe the rain, and so suggests slight doubt:
There is a similar effect from adding "I'm sure..." or "... definitely ...". The fact you feel the need to say "I'm sure" actually makes it sound less certain. Compare:
Saying "The Smiths must have bought this house" means that you have worked it out from evidence and reasoning. It is close in meaning to "I'm sure that the Smiths have bought this house." I'd accept it as a reasonable paraphrase, though not exactly the same.