Why do "supposed" and "expected" both have similar dual meanings of assumed/predicted or obligated?

"You are supposed to pay your taxes"

This could mean that you should pay your taxes, under obligation. It could also mean that someone (probably the speaker) has presumed that you do pay your taxes.

"You are expected to pay your taxes"

Again, this could mean that you should pay your taxes, under obligation. It could also mean that someone (probably the speaker) has presumed that you do pay your taxes.

I've always been fascinated, and annoyed, at the dual meaning of "expect". The presumptive meaning of "suppose" is rare in modern English, so this parallel hasn't been clear to me until recently.

Why would these two different words be synonymous for two different pairs of meanings?

Because sposta and expected to are modals, and all modals have both a deontic sense -- obligation -- and an epistemic sense -- assumed/predicted. Just like must can be "obliged" as in You must attend the meeting (deontic), but also "assumed/predicted" as in This must be the place (epistemic).

Quoted from @JohnLawler's comment on this question.