In constrained optimization, an active constraint is generally taken to mean one whose inequality sign can be changed into an equality sign without affecting the optimum. However, I would like to have a term to mean a constraint which would lead to a different result if it were not present.
Case in point: $$ \min x^2 + y^2 \\ \text{s.t.}\ x + y \geq 0 $$ What should I call the constraint $x+y\geq0$ if I want to say that it wouldn't have made a difference if it were not present?
Active means that the solution changes if the constraint is removed. What you want is the following Active and tight vs active and not tight.