When calculating the extremas, is there really a difference between relative and absolute extremas? Or are they just used interchangeably?
absolute means global. It's possible to have several relative extrema, and some, all, or none may be absolute extrema.
A parabola has one relative extremum, which is absolute.
A cubic such as y=(x-1)(x-2)(x-3) has two relative extrema, but no absolutes at all, since the function goes off to infinity in both directions.
a quartic like y=(x-1)^2 * (x-2)^2 has 3 relative extrema; one max and 2 min, but only the minima are global since y goes off to +infinity, but never gets less than zero.
Start tossing in exponentials and logs, and trig functions, and things can get complicated.