Does a copy of a permanent enter the battlefield or is it already there when it becomes a copy?

There are two distinct ways a permanent can become a copy, and they work very differently. Understanding which one is happening is essential.

Effect on an existing permanent: If a spell or ability says something like 'becomes a copy of' targeting a permanent already on the battlefield, no zone change occurs. The permanent is already on the battlefield and simply has its copiable values overwritten (CR 706.9). It does not enter the battlefield again, so 'enters the battlefield' triggered abilities do not trigger.

Token or spell that enters as a copy: If an effect creates a token that is a copy of a permanent, or if a spell resolves and puts a copy of a permanent onto the battlefield, that new object does enter the battlefield (CR 706.10). This means any 'enters the battlefield' triggers will fire for it, because it is genuinely entering a new zone.

The key rule governing what values a copy has is CR 706.2, which defines 'copiable values' as the printed values plus any copy effects, but not counters, damage, or other non-copy modifications.

Example: Suppose Clever Impersonator enters the battlefield and you choose it to be a copy of your Mulldrifter. Clever Impersonator enters the battlefield as a copy — it is a new object entering, so Mulldrifter's 'enters the battlefield' trigger fires and you draw two cards. Contrast this with Cytoshape making your existing Grizzly Bears become a copy of Mulldrifter: the Bears are already on the battlefield, so no ETB trigger occurs.