What is different between: like verb+ing and like to verb ? Do we also use this rule with verb love and hate?
Thanks for help.
The two forms are basically identical -- saying "I like running to the park" and "I like to run to the park" are going to carry exactly the same meaning.
I only difference I can think of is using like verb + ing instead of like to verb if the sentence is very short, for example "I like running" is probably more commonly said than "I like to run", although the latter is by no means uncommon. In the same way, like to verb is probably more common if there's a lengthy part of the sentence that follows the verb.
I think it makes a difference only in very specific interpretations. If I like running, I like to keep running while running, but if I like to run, I don't like the process too much, but I can appreciate the associated value, so I look forward to it (to-ward). Combined that gives "I like to run and feeling all exhausted and proud afterwards, but I don't feel liking anything at all while running". But this is a really flimsy analysis by myself that would work vice versa as well. I'm just trying to say there is opportunity to encode a deeper meaning, which probably helped a lot to create these constructs in the first place, but which is lost in imprecision.