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I shouldn't have talked back to him. I know where I stand.

I shouldn't have talked back to him. I know my place.

What's difference between the two sentences and the difference between I know where I stand and I know my place? In contexts like this, are they interchangeable?

These two idiomatic expressions have significantly different implications...

I know where I stand
I have a clearly-defined opinion (on some contextually-relevant topic).

Often carries the strong implication that I don't want to discuss the issue - because I've already made up my mind, so there's no point in talking to people who only want to persuade me to change my mind.

Effectively My mind is made up, and you will not convince me to change my opinion.

I know my place
I realise that I have low "social status" in the current context.

Often with the implication that I shouldn't say what I think (or even contribute to any debate on the current topic). I am expected to simply endorse the opinions of those with higher status and/or more power than me.

Effectively I am servile, and must do/think only what I'm told to by my superiors.

Given the preceding context (I shouldn't have talked back to him), the first example would normally be understood to mean that I shouldn't have wasted my time talking to him. Obviously he only wanted to engage me in debate in hopes of persuading me to change my position, but I was never going to allow that to happen anyway, because my position is "fixed, not up for debate".

The second example would normally be understood to mean that it was socially / politically unwise of me to disagree with him - because he has more power than me, it was dangerous / impertinent of me to challenge him.

EDIT: This question obviously generates a lot of interest, so I thought it might be useful to consider the far less common assertion I know my position, which could be used with either of the above senses...

Personally, I feel that the two different idiomatic meanings aren't entirely arbitrary - the reason they've been assigned this way is at least partly because to stand is normally a voluntary act (often against resistance - consider withstand, stand up to, take a stand). Whereas to be placed [somewhere] is effectively a "passive (servile)" action.

As a class-obsessed Brit, I can't resist adding a link to the classic I know my place comedy sketch (from The Frost Report, 1966, with John Cleese, Ronnie Barker, and Ronnie Corbett), where physical height is amusingly conflated with social status. British humour at its best!

The idiom "know where you stand" has at least three possible meanings ...

• Knowing what your opinion on a subject is;




• Knowing what your situation is, and in particular what your responsibilities are; and



• 
  

  Knowing how someone feels about you;

  
  
  

  ... but none of them are the same as "know my place", which is

  
  



• Accepting a subservient position within a social group.

How you should interpret the particular examples you give in the question depends a bit on the exact scenario, but in a typical case both sentences might mean that talking back was a poor decision because the person you were talking back to had authority over you. However, the first phrasing suggests that you are only concerned about the risk of retaliation, whereas the second suggests that you actually believe that it was wrong of you to talk back under the circumstances.

I shouldn't have talked back to him. I know where I stand. - talking back to him was unwise, because it wasn't going to achieve anything and he might retaliate against me.

I shouldn't have talked back to him. I know my place. - it was socially unacceptable for me to talk back to him under these circumstances.

While there may be some situations in which the two idioms have more nearly the same meaning, they are unlikely to be completely interchangeable in any realistic scenario.

In response to your comments on the other answer:

What's your place in your family? - this is not an example of the "knowing your place" idiom. Here, the question is more literal: what position do you hold? I'm not sure a native speaker would be likely to ask the question in this way, but it would probably be understood.

Where do you stand in your family? - no native speaker would put the question in this way and it might be misunderstood as asking how your family feels about you.

When someone is misbehaving with him [John] just accepts it because he knows where he stands - implies that John does not care about the misbehaviour.

When someone is misbehaving with him [John] just accepts it because he knows his place. - implies that John feels that he cannot complain about the misbehaviour because of his inferior social position.

"I know where I stand" can mean something similar to "I know my place". The meanings mentioned by other answers are also possible interpretations. Disambiguating what meaning is meant becomes easier if the phrase continues for a few more words:

"I know where I stand on gun control" would mean you know what your position on that issue is.

"I know where I stand with Alice" would mean you know what Alice's opinion of you is (and generally suggests that the opinion isn't favorable). This might be related to the other meaning, in that "I know where I stand with Alice" means roughly the same as "I know where Alice stands on me", although the latter isn't a phrasing I've ever heard. This meaning could also be used with respect to a larger group, e.g. "I know where I stand in the company".

I agree Kevin's comment on another answer that "I know my place" suggests subservience and acceptance of your place, while "I know where I stand" is more likely to be defiant (or perhaps bitter), although this depends somewhat on tone of voice.

In your specific example of "I shouldn't have talked back to him", the two sentences are largely interchangeable, but "I know where I stand" fits slightly better if the reason is due to his personal opinion of you, while "I know my place" is better if it is your relative social standings that are the issue.