Does the Cellar count as the Basement?

Question

I'm trying to unlock The Lost so I would like to know, if I die by a Mulliboom in the Cellar, is it the same as dying in the Basement by a Mulliboom.

Answer 1

Yes, evey step to unlock The Lost can be done in the alternative stage as well.
(Source (Spoilers))

Answer 2

Floors are divided into different chapters (Chapter 1,2,3,etc). Each and every one of these chapters consist of 2 floors. The Cellar can replace The Basement (if you've unlocked it), it's just a more difficult version essentially. But it's still "Chapter 1", which is required for the first step in unlocking The Lost. This also means that achievements that are acquired by not taking damage (Basement Boy, Spelunker Boy, etc) aren't affected by whether or not you end of on The Cellar or The Basement.

TLDR; It's chapter-based. 1 chapter = 2 floors. Chapter 1 = The Basement/Cellar 1 & 2. Most unlocks related to floors are based on the chapter rather than the actual "floor-version".

Sources: Chapters, Achievements. "Basement Boy" being number 37. Rebirth wiki works fine when it comes to these specific things but isn't the most reliable when it comes to certain things such as Items for example.