Does "each creature" include all creatures on the battlefield?

Question

I'm referring to Pyroclasm. I want to make sure it deals damage to all creatures on the battlefield.

Answer 1

Barring multiplayer range of influence rules (see comprehensive rule section 801), each creature means that each (therefore, every) creature on the battlefield will be dealt damage.

If you're interested in the nitty-gritty comprehensive rules which spell this out, this is a consequence of comprehensive rule:

609.2. Effects apply only to permanents unless the instruction's text states otherwise or they clearly can apply only to objects in one or more other zones. Example: An effect that changes all lands into creatures won't alter land cards in players' graveyards. But an effect that says spells cost more to cast will apply only to spells on the stack, since a spell is always on the stack while a player is casting it.

Knowing:

110.1. A permanent is a card or token on the battlefield. A permanent remains on the battlefield indefinitely. A card or token becomes a permanent as it enters the battlefield and it stops being a permanent as it's moved to another zone by an effect or rule.

Also remember:

119.1a Damage can't be dealt to an object that's neither a creature nor a planeswalker.

A particularly tricky opponent could Ghostly Flicker their Blinkmoth Nexus in response to your Pyroclasm and save it. When the 'Flicker resolves, the Nexus would return to the battlefield having no memory of being a creature a moment before.

Answer 2

Yes.

"creature" means "creature permanent" which means "creature card or token on the battlefield".

109.2. If a spell or ability uses a description of an object that includes a card type or subtype, but doesn’t include the word “card,” “spell,” “source,” or “scheme,” it means a permanent of that card type or subtype on the battlefield.