Be supposed to and its meanings

Merriam-Webster [augmented, especially with further examples, below] asserts that there are six, not just two, senses that should be distinguished.

The ones showing deontic modality (moral obligation; permission) are

be supposed to ...

[4] —used to say what someone should do ...

• I'm supposed to clean my room before I go outside. ...

[5] —used to refer to what someone is allowed to do [used in a negative, sometimes interrogative, context]

• We were not supposed to leave the room.

• [Are we supposed to be doing this?]

The other senses convey [1] expectation of a future event, [2] intent, [3] irritation (a pragmatic usage), and [6] modality in the sense of received wisdom.

[1]: to be expected to do something [ie occur]

• [It's supposed to rain tomorrow.]

[2]: to be intended ... to be something

• The party was supposed to be a surprise [but Tom let the cat out of the bag].
• [This soup is supposed to be hot.]

[3] —used [intensifyingly] to show that one is angry or offended[, irritated], by something ...

• "Well, you've done it again."                "What's that supposed to mean?"

[6] —used to indicate what people say about someone or something ...

• That breed of dog is supposed to be good with kids. [alleged/reputed]

...............

In the above, care has been taken to (hopefully) distinguish the senses M-W considers independent. A problem to be avoided is using say 'expected' carelessly in a definition, as it itself has both deontic and epistemic senses.

• 'You are expected to wash your hands before eating.'

• 'It is expected to arrive by Friday.'

OALD proposes also two definitions, essentially, but they are different. There is a third one that concerns the negation of this expression, and it is of interest as well, specially in the light of the fact that it is not a negation of the first definition. Let's say first that in either three cases of definition, "supposed to do" is an idiom.

to be supposed to do/be something

1. ​ to be expected or required to do/be something according to a rule, a custom, an arrangement, etc.

• What am I supposed to do?
• You're supposed to buy a ticket, but not many people do.
• I thought we were supposed to be paid today.
• The engine doesn't sound like it's supposed to.
• You were supposed to be here an hour ago!
• Oops—that wasn't supposed to happen.
• How was I supposed to know you were waiting for me?
• ‘Yes and no.’ ‘What is that supposed to mean?’ (= showing that you are annoyed)

2. to be generally believed or expected to be/do something

• I haven't seen it myself, but it's supposed to be a great movie.
• This combination of qualities is generally supposed to be extremely rare.
• She's supposed to have had hundreds of lovers.

not be supposed to do something

1. to not be allowed to do something

• You're not supposed to walk on the grass.

In "1." of the present definition "according to a rule, a custom, an arrangement, etc." is very important. It shows that the expectation depends on rule, custom, arrangement, etc. ("be expected to do/be"; paraphrasing: "should do/be"). In "2" the definition is based on expectation, but this time the expectation stems from what is generally believed; "should" as used in this case embodies the expression of hypothetical knowledge that stems from general knowledge ("The weather should be fine tomorrow. (from a knowledge ot the weather forecast)"). This precision is lacking in the OP's "2". (A careful examination of the examples should drive home the certitude that two definitions are involved.)

This OALD definition should show that the two definitions are not one, and that if they can so be conceived, the reason of it is merely due to imprecisions of language.

An expectation is more like a prediction. It can be used with both animate and inanimate objects e.g.

It's supposed to snow in winter, not in summer.

If you let go of a ball, it's supposed to fall.

Definition 2 is mainly used to refer to requirements of animate objects, usually people with free will.

Students are supposed to pay attention to their teacher.

The expectation can have a different basis:

Expectation based on a published schedule:

Do you happen to know when train arrives? I'm from out-of-town.

--It's supposed to arrive at 9:15, having left the station at 9:00. But it's often late.

This train is supposed ^{expectation based on a commitment to schedule} to depart at 9:00 sharp and so the train crew is supposed ^{expectation based on employee obligation} to arrive at work in time to meet that schedule! This is your last warning. Next time, you're fired. No more "eye-opener specials" at Moe's bar, you hear me?

P.S. There was a bar near my high school that opened first thing in the morning. They advertized an "eye-opener special", a mug of beer with a whisky chaser.

The Wiktionary entry on supposed to does a pretty good job differentiating its meanings without relying heavily on the idea of expectation, and also includes the possibility of dynamic modality!

1. Required to, obliged to, ought to.

I am supposed to report to the police every week.

Paul is supposed to call his mother every day.

The phone is supposed to come with a manual.

2. (in the negative, preceded by "not") Permitted to.

You are not supposed to smoke in the restaurant.

[Note: this means, you are obliged not to smoke.]

3. (in interrogative or similar situations) Able to, capable of (used to indicate that an expectation is impossible or unreasonable in the context).

How am I supposed to work in all this racket?

What was he supposed to do—just sit there and do nothing?

4. Believed to; generally considered to; considered likely to.

It's supposed to rain.

The movie is supposed to be good.

The thief is supposed to be hiding in the forest.

5. Intended to; meant to.

The phone is supposed to save us time.

Is that supposed to be funny?