I am (not) supposed to do something means either a) I am (not) expected to do something ' I am supposed to get home early today' (= my family is expecting me home early today) b) I am allowed or not allowed to do something. 'I'm not supposed to stay in the office after the building has closed.' (= I don't have permission to stay) or c) I should or shouldn't do something ' 'I'm supposed to clean my room before I go outside.' (=My parents say I have to clean my room before I go outside) We can also say 'I should clean my room before I go outside.' 'I should do something' also means a) it is proper or correct that I do it 'I should write to her and apologise.' b) it is the best thing to do. 'My friends say that I should leave my boyfriend.' c) it is my opinion that.. 'I should go on a diet.' In British English we also use 'I should do' something to say what you want to do or want to have done. 'I should like to call my lawyer.'

There are very similar in meaning in English as well. 'I should' indicates the obligation to do something from one's own point of view ,it is more of a personal choice to do something. It has another meaning too ,when it forms the subjunctive mode. "If I should come late, go without me." 'I am supposed to' refers more to the collective conscience obliging the person to do something, as if you are saying : ' I am expected to do so ....' Inspite of the fine differences they could in one sense be used interchangeably.

In English I Should means Morally i am expected to do something on my on behalf I am Supposed to means I am expected to do something by others.

Put it simple: Grammatically, active/passive. Practically, no.

SHOULD-what is the best or right/important thing to do.... Eg; I am not very well.Perhaps i should see a doctor. SUPPOSED TO/BE SUPPOSED TO-when we are talking about the normal or correct way of doing things. Eg; I am supposed to buy tickets for my parents.