each other or together

Is there any difference between them?
We belong to each other.
We belong together.
They gave each other a flower.
They gave a flower together.

The first two examples are both correct. Although they mean almost the same thing there is a little difference. The best way I can describe it is:
‘… to each other’ - I belong to you and you belong to me.
‘… together’ - We should not be separated.

‘They gave each other a flower’ is correct, but ‘They gave a flower together’ is grammatically incorrect. An alternative way of writing ‘They gave each other a flower’ would be ‘They each gave the other a flower.’

Hi Dear B…,
Thanks a lot!!!