Hi Sergii,
First, yes there is a difference - no two words are the same..
I've tried to thing about this a lot and my best explanation is that 'for instance' is to give an example of something, but 'for example' is when you are explaining something. For EXAMPLE; when you say 'there are some serious things wrong with my car, for INSTANCE; the ignition button doesn't work'
The one was me explaining something to help you understand, the second wasn't.
:)