Sherlock Holmes used abductive reasoning.
Deduction: cause + deductive rule -> effect
Induction: (cause + effect) x many times -> deductive rule
Abduction: effect + deductive rule -> possible causes
A neat thing about reasoning is that we tend to use all three, too. Abduction → Deduction → Induction ... in cycles.
More on topic with the OP: to me, intuition is what happens when we skip through these steps. It's the heuristics we use to make good decisions when we don't have the time to "abduce" possibilities, "deduce" the likely answer(s), and "induce" the evidence of our deductions.
Seems like OP has fallen into that trap.
For whatever it's worth, I don't think Inspector Lestrade would appreciate the difference, so Holmes needn't bother either.