Specifically in the conversion of a haloalkane to an alkene, i believe this is the reaction mechanism.
Extrapolating on this, do all elimination reactions function as such, or is the term elimination reaction a reference to the ends rather than the means?
Elimination refers to the ends rather than the means. On top of that, it does not necessarily refer to the loss of a proton + a leaving group; it can in general refer to the loss of any small molecule. So, for example, a loss of CO2 is also considered an elimination, even though there is no proton there.
As far as proton + leaving group eliminations go (elimination of HX), the order in which the leaving group leaves and the proton falls off determines what type of elimination it is.
The leaving group can leave first - that is called an E1 elimination.
The proton can fall off first - that is called an E1cb elimination.
And if both of them happen at the same time, it is an E2 elimination.
