In fairness, FFXIV is my first MMO and I picked up those specific terms pretty quickly, since they're (generally) pretty straightforward. It's not like you're calling a cat a "fluffy thing"

You're calling "a series of skills used in sequence" a "rotation"
You call the "first sequence of abilities you use at the start of an encounter" an "opener" or "opening rotation"
You call the "sequence of skills you use to attack a single target" a "single target rotation"
The one I can see being confusing is the AoE Rotation one, since I picked up AoE = Area of Effect a long time ago from FF message boards.

I feel asking someone who is writing a guide to spell out these things for a new player is a little silly when the context provides a better explanation than any definition you can give. When a guide says:
"The basic Dragoon Rotation is:
HT>ID>DE>CT>4th>PH>TT>VP>FT>4th>repeat"

It is heavily implied by this what "rotation" means. Reiterating it later via "A Rotation is a string of skills you use in sequence to attack an enemy" is redundant, imo.

I learned what a "Rotation" is by looking up the old Dragoon: A Rotation Reborn thread way back when.