I suppose if it was written on a piece of paper, we could write them all on top of one another and do them at the same time
This is kind of what I'm driving at.
For riding, I don't consider myself Western or English. I tend to prefer western, but my horses have short backs and tall withers - good luck finding a saddle. I have one that mostly fits the two larger horses.
My favorite is Australian, but as I play around with it more, I'm getting better responses from my horses riding my Aussie saddle in a more forward seat...not jumper style, but much more forward than western.
And my new mustang is a short-backed, 13 hands BLM pony. He's always been ridden in a western saddle, which may explain his grouchiness when mounting...even my Arab saddle hits his hips. So he is now being ridden exclusively with my Bates jump saddle. The first time I put him in it, he bolted as soon as my butt hit the saddle. We did 3 laps at a gallop, 3 at a canter, then he slowed, shook himself, and seemed to say, "Hey, this works!" He is now acting quite happy with the jump saddle - but that requires me to practice things I hadn't done in over a year. His trot is un-post-able - his little legs move like a sewing machine needle, while his back rolls around like a drunk sailor on the second night of shore leave. It makes practice a two-point...interesting.
So do I ride western, English, Aussie? Or am I just confused?
In any case, when I go out to ride, I usually have an objective in mind - for either me or the horse. Warm-up depends on what I'm doing. We'll always start at a walk, so I can stretch my legs and the horse can settle. While both of us start to relax, I'm checking the horse for responsiveness to cues - seat, leg, reins, in that order. That may require a little remedial work. I'm also checking to see if my straight lines are straight, and my turns coordinated (which seems more accurate a term for my use than collected).
Impulsion comes afterward. I don't ask or want explosive acceleration at the start, although I sometimes understand a horse being nervous about something new. But after straights and turns at a walk, we'll go to trotting (usually with plenty of turns). I don't normally care for much collection, but 'gathering' himself and getting ready for sharp turns and sudden acceleration comes at the end. By that time, I figure I'm past the warm-up stage and into the real riding stage.
About 80% of my riding is bitless, so technically I rarely want him 'on the bit'. But a bit is an input device, as is a rope halter with reins, as are seat & legs...and I always want him "on the aids" or "on the cues" - listening to my input and responding. That is a part of our walking warm-up, and sometimes tells me I need to focus for a while on getting him to listen to my legs.
For my riding, I leave impulsion near the end, and collection isn't exactly on my list. The rest seems to be something you would be checking and working on every moment of the ride.