I think like this:
Go to bed : action of going to one's own room and lying down on the bed.
Go to sleep : I'm already in my room and lying down on my bed. And at some point I fall asleep.
Sleep : in the state of being in dream. this is not a point but duration.
With this, I made a story.
I usually go to bed around 10 but go to sleep(fall asleep) about an hour later. And I sleep for about 8 hours.
Am I right to think this way?
Those are perfectly accurate definitions.
Do be aware, however, that sleeping isn't always necessarily done in a bed (so just saying 'I went to sleep at 10' doesn't guarantee you went to bed beforehand) and that in my experience at least, if you don't specify the actual time you went to sleep, it is assumed that you went to sleep at about the same time as you went to bed.
I think your example sounds best and most natural if you just make the one change to use "fall asleep" as you have in parentheses:
I usually go to bed around 10 but fall asleep about an hour later. And I sleep for about 8 hours.
