Gerund: verb + -ing used like a noun. Example: I enjoy cooking.
Infinitive: to + base verb. Example: I want to cook.
No big meaning change: like, love, hate, start can often use either form. Example: I started learning / I started to learn.
Meaning changes: remember, forget, stop, try can change meaning.
Examples: I stopped smoking = I quit. I stopped to smoke = I paused another activity so I could smoke.