TITLE: Preschemes and schemes
QUESTION [8 upvotes]: This is a very minor point, but one which had been grating me for a while. I apologize for asking a relatively trivial question, but nevertheless hope that it is suitable for MO since it should have a definite answer.
In Mumford's books, for instance Curves on Surfaces or Red Book, there is thing called "prescheme" which looks like a scheme, and scheme is something else.
But this terminology does not seem to be used elsewhere, and if at all is the case, prescheme seems to be something cruder than scheme.
I will be grateful for clarifications regarding this terminology. "Curves on surfaces" is a nice book, but whenever I pick it up I find myself wondering about this without any avail.

REPLY [9 votes]: In the 1971 edition of EGA (this is a revised version of the original 1960 EGA) you can find the following remark in the introduction:
Signalons enfin, par rapport à la première édition, un changement
important de terminologie: le mot «schéma» désigne maintenant ce qui
était appelé «préschéma» dans la première édition, et les mots «schéma
séparé» ce qui était appelé «schéma».
The 1971 terminology should be standard today.