Gerunds are noun forms and infinitives are verb forms.
In the simplest form, nouns are people, places or things; verbs show action.
Look at this:
What is the meaning of a gerund? You use a gerund to mean a thing.
Meaning is a gerund (has a -ing ending) and to mean is an infinitive (has a to- in front of it). Do you see how meaning acts as a noun? Do you see the article the in front of it? You can't put a the in front of an infinitive, for example.
I enjoyed the choir's singing (singing is a noun, a gerund noun; you could replace it with " robes" for example). I enjoyed the choir's robes.
I want to sing with the choir. (to sing is an infinitive; you can replace it with another action verb: I want to run with the choir, to sit with the choir, to pray with the choir. You'll usually find a simple verb in front of an infinitive (in this case, want; in my first example, you use a gerund to mean... the simple verb is use. )
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