I like to do/doing

Some of the don't change the meaning but the others do. The only way I could suggest you that you should memorise them or at least know the key rules for some verbs. As for your examples, there is no change in the meaning.

Have a lok at this link:

You had better make a search about gerunds and infinitives or -ing/-t

Anonymous
I'm never sure how I should use a particular verb. For example - which form of these two is correct:

I like to play piano.

or

I like playing piano/football etc.?

How do I know whether I should use gerund or infinitive?

As far as the “I like…” context goes, most of the time, either way works just

GoodmanI like to invite / inviting Paul to my party.

That sentence doesn't really make much sense with 'like'. It seems to me you must have been thinking of would like rather than like in that example:

I'd like to invite

You are right! I missed the contraction of "would". I stand corrected.