infinitive vs gerund

[adullstudent]

hi.what is the difference between these sentences?
do you like to swim?
do you like swimming?

i stopped to swim.
i stopped swimming.

i hate to swim.
i hate swimming.

i've started to swim.
i've started swimming.

and is there any rule for verbs like these that can be followed by both infinitve and gerund?

thanks.

[Tdol]

1 Like to do- in British English, we use this for a restricted pleasure- I like to swim in the sea, while we use the gerund for general pleasure- I like swimming. In American English, I believe there is less difference. (Hate would folow this pattern)
2 Stop
I stopped swimming = no more swimming
I stopped to swim- I stop one thing in order to swim