There are two types of drumming -- layered and linear -- and they are very far apart in every way.
Layered drumming is what we all do most of the time: bass drum on 1 and 3, snare on 2 and 4, ride rhythm on top. The instruments and the figures are in layers: a layer of cymbal, below that a layer of snare, and a layer of BD as a foundation.
Layered drumming requires a lot of coordination. It also requires the ability to play at least a couple of ostinatos at the same time. An ostinato is simply a repetitive pattern: ba-bump/ba-bump/ba-bump on the bass drum, ding-dinga-ding on the cymbal. The idea here is that some limbs will play an ostinato while other limbs might play in a less regimented manner. Most rhythms are just a pile of ostinatos.
The rule for linear drumming is that no two limbs will strike at the same time. Traditional drum training has neglected linear playing, but it is coming on strong. Linear style can range from the simple to the complex. Usually the practitioner will work out a number of interesting patterns and intermingle them in a tune. So our layered rock beat can be reinterpreted as linear: BD Cym SN Cym / BD Cym SN Cym / BD Cym SN Cym.
Linear playing will take some work to master, and because it is radically different from what you're used to, your existing technique may get in the way from time to time, so one of your objectives is to unlearn the old ways. One of the best books for this is "4-way Co-ordination" by Dahlgren & Fine.
Another approach you might try is mixing things up with ”Stick Control”. Alan Dawson reinterpreted “Stick Control” by playing the R strokes with alternate sticks and the L strokes on the bass drum. So a paradiddle -- RLRR LRLL -- would yield RH BD LH RH / BD LH BD BD. You can take it a step further by alternating feet as well. Try this: play your right hand on the ride cymbal and left hand on the snare. For R, play alternate hands; for L, play alternate feet. So our paradiddle now becomes Cym BD SN Cym / HH SN BD HH.
You don't have to play linear patterns all the time. Even a little bit of linear variation can add interest to a conventional rhythm. Plus working on linear patterns will help free your limbs to do more interesting ostinato patterns.
4-Way Coordination: A Method Book for the Development of Complete Independence on the Drum Set, by Marvin Dahlgren & Elliot Fine
Stick Control For the Snare Drummer by George Lawrence Stone, 1935