TITLE: Terminology introduced in recent years with more than one meaning
QUESTION [5 upvotes]: Suppose a term(inology) is recently (in last 20 years) introduced in research mathematics.
It might happen that some one who wish to use it, in the same area of research, for different purposes or see from different point of view realize that, some condition needs to be added or removed for their pov/purpose but still calling by the same name. This creates a slight confusion.

What are some term(inology) introduced recently (in last 20 years) which have more than one possible meaning because of different point of view or different purpose?

REPLY [3 votes]: My vote is for the phrase "normal Cayley graph".
Recall that a Cayley graph Cay($G$,$C$) is obtained from a group $G$ and a subset of its elements $C \subseteq G$. The vertex set of Cay($G$,$C$) is $G$ itself, and for each $g \in G$ and $c \in C$ there is an edge from $g$ to $gc$. 
Some of my colleagues and co-authors say that Cay($G$,$C$) is a normal Cayley graph if $G$ is a normal subgroup of Aut(Cay($G$,$C$)).
Another set of colleagues and co-authors say that Cay($G$,$C$) is a normal Cayley graph if $C$ is closed under conjugation, (so that $C$ is like a normal subset of $G$). 
The first usage involves looking outside $G$ while the second usage involves looking inside $G$.