Do you like to watch TV?
Do you like watching TV?
Do you like hitting people?
DO you like to hit people ?
The verb LIKE can be followed by either an infinitive (to—) or a gerund (—+ing). The meaning is the same.
As far as I can see they are all different ways of saying something.
All saying the same thing but saying it differently.
No difference. Some verbs can be followed by either the infinitive or the present participle without a change in meaning. “Like” is one of those verbs.
Others can only be followed by the infinitive or the present participle:
He wants to watch TV.
Others change meaning:
He stopped watching TV. (he is no longer watching tv)
He stopped to watch TV (he stopped some other activity and started watching TV. )
There’s no difference between the first two.
There’s no difference between the second two.
They are alternative ways of saying the same thing.