I tend to use should when it’s a suggestion I don’t have a strong opinion on, i.e. it could be done in many other ways than the one I’m suggesting and it can still happen.
You should stop by that gas station to go to the bathroom.
On the other hand, I usually use must for things that have to happen in a certain way; any other way would make that thing not to happen. The problem is that some people find this usage harsh, as they receive it like if I’m giving them an order.
You must cross the street to get to that store.
To me, it’s just a depiction of reality, not an order. But I’m neither a native speaker nor a regular person. 🙂
So, what’s the proper use for must and should? Does this use differ among the English dialects?
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.