When to use infinitive and when to use present participle of a same word?
I like to play cricket.
To play cricket is fun.
I love playing cricket.
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In the first case of I like to play cricket simply indicates that it's my intention to play cricket in a certain situation/condition.
It also means that I prefer cricket to other sports.
In the second case: I like playing cricket means it's my passion/hobby/regular habit to play cricket.
In detail such a grammar topic is only to find in a grammar, e.g. in The Oxford Guide to English Grammar. Section 121 has the title "To-infinitive or gerund after a verb", 3 pages. This grammar has a detailed list of
1 verbs connected only with to-infinitive
2 verbs only with gerund
3 verbs with both possibilities (almost no difference)
4 verbs with both possibilities, but different meaning.
The grammar point verb patterns or verb construction covers an enormous area and the more one advances in English the more important this chapter becomes. Unfortunately this grammar sector isn't yet presented in an optimal manner. There is still a lot to do. If in doubt whether the construction is "to avoid doing" or "to avoid to do" you best look it up in dictionaries such as OALD.
It depends on the verb. Certain verbs expect certain kinds of arguments.
The verb "want" expects an infinitive: "I want to play cricket." For this verb, a gerund on its own doesn't work: *"I want playing cricket." However, a gerund with an infinitive complement does work: "I want playing cricket to be included in the festival's activities."
The verb "enjoy" expects a gerund: "I enjoy playing cricket."; For this verb, an infinitive doesn't work: *"I enjoy to play cricket."
The verb "like" is happy with either gerunds or infinitives. Both "I like to play cricket" and "I like playing cricket" are acceptable. To my ear, there's no real difference in meaning.
Sometimes the choice between gerund and infinitive does change the meaning. "I regret informing you" means something close to "I regret that I have told you something." On the other hand, "I regret to inform you" means something close to "I regret having the responsibility to tell you something."