Not "how many cycles until failure" — that's the symptom. The real split is whether the material plastically deforms every single cycle.
Fatigue itself is cyclic-stress-driven crack growth — a completely different mechanism from creep, which is steady-stress deformation. But fatigue itself splits into two regimes that behave, and are analyzed, very differently. High-cycle fatigue (HCF) runs at low stress amplitudes, well within the material's elastic range, and takes a large number of cycles — typically more than 104–105 — to initiate and grow a crack to failure. Low-cycle fatigue (LCF)runs at high stress amplitudes that push the material past yield on every cycle, generating a small amount of plastic strain each time, and it fails in far fewer cycles as a direct result. The dividing question isn't "how many cycles will this take" — that's the outcome. It's "is the strain each cycle elastic, or does it include a plastic component," and that determines which design method actually applies.