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.



Preschemes and schemes
The prescheme usage is outdated. As indicated in [nLab](https://ncatlab.org/nlab/show/EGA),



> 
> our schemes are in EGA called preschemes; EGA’s schemes are what we call separated schemes
> 
> 
> 


