The biggest characteristic of the drums that defines each part is the base drum, or the kick pattern.
A good drummer will learn the drum part verbatim for every song their worship leader gives them, and focusing on the kick drum will note how it changes for each part of the song. The transitions between parts (e.g. verse to chorus) must be smooth.
The kick pattern is essential to supporting whatever section your in.
Knowing what your going to play before you move in to the next section is vital to keeping the whole band lock in. It keeps trust within the band.