Horizontal push, Horizontal pull, Vertical push, vertical pull & legs - anything ive missed?
flexion, extension, abduction, adduction, protraction, retraction, elevation, depression, medial rotation, lateral rotation, pronation, supination, circumduction, opposition.....
It is pointless to try and create a training routine around "types of movement".
In these types of programs, "legs" are usually further divided into hip-dominant (deadlift variations) and quad-dominant (squat variations).
What's the goal of your program, since you're looking to use these categories?
True, "types of movement" is a pretty broad description. But generally, if we're not talking about bodypart or full body splits, planes of movement are the next option, and I think that's what he meant. Someone could be extra-nitpicky and include some type of rotation work, but that's overly-specific considering the relatively-limited exercise options.
It is more productive to think in terms of muscles used, and whether they are used hard or not that much in the exercises done.
It's common for a split routine, unless there are a lot of rest days in the rotation, to have some muscle worked fairly hard two days in a row. Which all else being equal one strives to avoid.
But you can't get around it, other than having working in more rest days than may be optimal.
So just be aware of it, try to minimize it, see if it's causing a problem that you're having, and from time to time switch things up so that this occurs somewhere else.
For example, it's common for rear delts to get worked hard two days in a row both if back and shoulder day are right up against each other. Perhaps you might want to switch things up if you've been doing this for a while and suspect it may be holding back the rear delts.
Of for example in an upper/lower split, or some other splits, deadlifts and upper back training might be on adjacent days. Same situation: some muscles in the upper back are getting hit twice in a row. That doesn't mean it's an unworkable split, but be aware of it.