Do drummers count drum beats separate for each limb, or coordinated all together?
Limb independence is essentially the ability to improvise with a given limb over the drum pattern you are playing. It is a developmental goal of drumming, not a foundational approach. The easiest way to learn drum patterns is the way most people have described already. You have to break down the pieces at first, but it only becomes a beat when everything is coordinated and happens at the same time, every time. This is basically the opposite of limb independence, and the drawback is that in order to change the pattern of any one limb, you essentially have to learn a whole new pattern on all four limbs. Something as simple as adding an off-beat bass drum hit can put you back at square one. Once you develop a small amount of limb independence, from playing enough different types of patterns and beats, you can develop and learn new beats that much more easily. This is limb independence stage one. It’s what you need to pull of a spontaneous drum fill or to pick up on the bass guitar/rhythm