When should one use "should" and when should one use "must"?

Solution 1:

There isn't really any vagueness about when to use must and when to use should.

Must always implies absolute obligation or certainty.

Should always implies a request, suggestion, or expectation although in some contexts a request may be so strong that it could be seen as an obligation.

See @Cerberus's excellent answer here exploring the "built-in slipperiness" of English words commonly used in the general area of volition/expectation - where must applies to both at the extremes of obligation/certainty. Things only really get murky at the lesser levels.

But OP's example 2 is structurally ambiguous - You must cross the street to get to that store could mean any of...

You are obliged/I order you to cross the street [and thereby to get to that store]

You would/will have to cross the street if you wanted/need to get to that store

More naturally we interpret the whole sentence as informational, with an implied if you want to get to the other side. The obligation implied by must doesn't come from the speaker - it comes from the laws of physics which say the only way to be on the other side of the street is to cross it.

Note that in practice, people often deliberately or unwittingly flout these distinctions. I'm sure the vast majority of people who have ever said, for example, "I must be mad!", or "We must have dinner together soon" didn't really mean they were absolutely sure, or imposing an absolute order.

Solution 2:

Here is my take on sentence #2. The word must can mean both your order and a necessity enforced by something else (physics, regulations, conventions, and so on). Therefore, if there is a possibility of confusion of the meaning of must, I think that have to is preferred when you mean a necessity.

But in sentence #2, I do not think that the meaning of must is ambiguous (unless you are in an unlikely situation where the store can be reached with or without crossing the street and you might be telling someone not to go to the store without crossing the street). Therefore I find nothing wrong about sentence #2.

(I am not a native speaker of English.)

Solution 3:

In general, "must" is more imperative than "should", which is often used as more of a suggestion.

Both give some scope for choice, since if it were an order then you'd drop them completely.

However these can both be used in speech such that these guidelines don't apply, in particular in a passive aggressive command.

Solution 4:

According to English Grammar in Use by Raymond Murphy (Second Edition), must and have to are used to say that it is necessary to do something. Sometimes it doesn't matter which one you use:

Oh, it's getting late. I must go/I have to go.

However, he goes on to explain that sometimes there is a difference and it's important to differentiate. must is personal; we use must when we give our personal feelings (The speaker says it is necessary.): You must meet her.

1. She's a really nice person.You must meet her.
2. I haven't phoned Ann for ages. I must phone her tonight.
3. I must get up early tomorrow. There are a lot of things I want to do.

have to is impersonal; we use have to for facts, not our personal feelings. You have to do something because of a rule or something:

1. You can't turn right here. You have to turn left.
2. George can't go out with us this evening. He has to work.
3. I have to get up early tomorrow. My train leaves at 7:30.

I first learned of this grammatical "rule" when I started teaching English in schools and at the university level in Germany, where much, if not all, of the educational materials for English are written by German and British authors. I can only say that I'm an American and have always said have to; must is simply not in my vocabulary.

Most of the American teachers and lecturers I know here in Germany say they hardly ever use must in the context being discussed here. The British ones, on the contrary, say they use must in the context when the speaker thinks it's necessary to do something - that is, when the speaker is expressing his/her personal feelings. They have admitted, though, that they learned the rule when they started teaching English abroad.

Maybe usage is different in North America, or maybe just in the US, although Canadian and US varieties of English are very similar.

Solution 5:

I fully agreed with the idea that the word "Must" implies absolute obligations and certainty.

But what exactly are the contextual conditions that enable one to comfortably use the word "Must" ?

1. Absolute obligations comes from authority.
2. Certainty comes from a strong and determine will and effort of the speaker to bring upon what he/she wishes to reality.

For the purpose of illustration, I shall give the following examples:

A Father may say,"Son, You must finish your breakfast before going to school." He uses his authority in the family to set forth certain rule in his household.

A Security guard may say, "Gentleman, you must not loiter around here which is a private property." By virtue of his role and position, he is determined to evict the loitering youth should he failed to comply.

In both instances, the word "Must" is meaningful, purposeful and can be carried out.

On the other hand, there are also frequent misused and abused of the word "Must" in the media. Let me illustrate with the following examples:

"No XXXX government will have any legitimacy without elections. Some leaders and parties are obstructing the electoral process as they have nothing to face the electorate with. But elections MUST be held",commented a long term XXXX expert.

"International community MUST also help in this respect wherever possible"