Learn English – “I wish I had not done something” vs “I wish I would not have done something”

Have done --- Have done is a present perfect tense, generally it is used when the action is completed recently/just now.

Had done-- Had done is a past perfect tense, generally refers to something which happened earlier in the past, before another action also occured in the past.

For Example:

We have done the work -- Here the action completed recently/just now.

My friend offered me an apple in classroom yesterday, but I wasn't hungry because I had just eaten lunch -- Here the action happened earlier("yesterday"), and another action ("I had just eaten lunch") also occured in the past.

Meaning: In the context of hair cuts specifically, you can use both without concerns as it is (usually) obvious that people get their hair done by others. (Unless it's very obvious someone did it themselves :))

However, in other situations (especially formal) I would be a little bit more attentive to which one of those I use:

Hey Sam, what about the mail I asked to be sent by this afternoon?

If Sam did it himself, he'd usually say:

I got it done

(If Sam doesn't have to use either of "got it/had it" he'd just say "I did it/I sent it" to avoid any potential confusion)

If Sam had someone do it for him, he'd usually say:

Don't worry, I had that one done / I had it done / I had it sent

Or

I got someone to do it for me

(more casually: I got someone to do it)

"Got it done" usually means that the speaker carried the action himself. "Had it done" almost always means that someone else had done it on the speaker's behalf.

Formality: "I got my hair cut" is the more casual way to phrase it.