Isn’t delayed auditory feedback similar to echo?

Yea it can basically short circuit your thinking when trying to talk, BUT oddly enough it helps with stuttering with a short enough interval. There's in-ear attachments people can use that do this exact thing and it helps reduce the amount of stuttering and the brain getting stuck on a sound. My brother uses one, its crazy how it works

If speaking strictly in terms of audio effects this is a delay, with "echo" usually implying feedback so the delayed signal is attenuated and fed back into the delay line, getting quieter each iteration and fading naturally.

Yeah, this immediately made me think of DAF.

My wife is a speech pathologist and hooked me up to a DAF machine for some research, and the effect was totally shocking to me as a layperson. I think I did worse than average, but I was basically unable to speak with delayed sidetone.

It's like a single bounce. Echo effects usually have multiple bounces, each quieter than the one before it.