Both are correct but have different meanings

Both are correct but have different meanings.

John enjoys (to play/playing) with my cat.

My manager suggested (to work/working) on the project together.

Both are the same but have different meanings.

I began (to ask/asking) questions about the situation.

Phillips hopes (to complete/completing) his project by the end of the month.

Both are correct and have the same meaning.

I plan (to visit/visiting) the United States next year.

I stopped (to see/seeing) my friend last weekend.

Jessica seems (to worry/worrying) about a lot of things.

She kept (to avoid/avoiding) (to answer/answering) my questions.

He claimed (to be/being) the best chess player in the world.

He claimed that (to be/being) the best chess player in the world would make him rich.

Bonus: She kept (to want/wanting) (to avoid/avoiding) (to answer/answering) my questions.

They decided (to read/reading) a book.