PvP in Halo Infinite

it will depend on the game.

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Good morning

In general all modes can be seen in the menu, but what game would it be?

The PvP Modes are:

Arena

BTB (Big Team Battle)

So any PvP tasks would likely need to be undertaken in one of those....basically, anything in the Multiplayer section of the game....unless the task says it needs competing in a specific mode of course

Are all the modes considered PvP, or just some?

Above statement is not necessarily true, I like BF but I also like Destiny pvp. Destiny is similar to Halo but it has a good bit of differences if you have any game rental places or options you might want to try it. I'm sorta decent at Halo but I'm struggling
in Destiny's pvp so your mileage may vary. The differences such as infinite grenades with a cool-down period after each, selecting your loadout and other things might help you or hurt you no telling.