I would propose that practice relates to working on actual music that you need to prepare for performance somewhere, such as for a lesson or for a concert. Warm-up is on the other hand a work-out designed to get you going before each playing session. One of the goals of a warm-up is also the continued development of underlying skills. Playing scales and working on technical skills are essential and clearly are a part of any warm-up routine.
Etudes can border the line between warm-up and practice, depending on how they are used. For me at this point in my career I often end my warm-up with an etude or two. Is this etude work practice, or is it warm up? For me it is more of a warm-up but for a student it could be practice.
One job of a good teacher is to assign materials that will build the technique of a student to reach the level needed to perform the music they hope to perform. Etudes and technical/scale studies are excellent cross training material for “real” music and are an essential component of any good daily routine.
As to warm-up itself, while I can play in a pinch without any warm-up, I very much prefer to fully warm-up. When I was a younger professional I warmed up about twenty minutes before every playing session on the same basic routine. Normally I tried to set my playing day up with two to three main playing sessions, each one preceded with the same warm-up. Now I vary the routine more and the warm-up is longer before the first playing session, aiming for a longer and deeper initial warm-up before I get to a day of practice and performance.