In the first written description of how to build a Beowulf cluster, by Radajewski and Eadline in 1998 [1], the management node was refered to as the "server node" and the compute nodes as "client nodes".
I believe the term "compute node" was first used in the context of the Intel ASCI Red supercomputer that was installed at Sandia in 1997. This later led to the Cray XT3, XT4, XT5 families of machines that used the same terminology.
But I believe the term was not in generic usage outside of those specific supercomputers until around 2005-2010.
[1] https://ibiblio.org/pub/Linux/docs/HOWTO/archive/Beowulf-HOW...
Mainframes use those names too. I'm not sure what name blade hacks use (yeah, I'm out of a datacenter for that long), but they have those things too.
For example, storage servers usually are full to the brim of harddrives and SSDs.
Then you might need to process your data on GPUs/CPUs where you have specific servers specced out with more CPU/GPU resources.