I think of "compute" as referring to the resources for computations, rather than the computations themselves. For instance "compute-intensive" for an algorithm

I think of "compute" as referring to the resources for computations, rather than the computations themselves. For instance "compute-intensive" for an algorithm means that it is expensive in terms of computation resources, i.e. CPU cycles, as opposed to say I/O or network usage or something. Sometimes it refers to the actual physical hardware, sometimes to the theoretical resource of CPU time.