Is this a distinction: "blow dry" suggests a shampoo is involved, but "blow out" could be styling dry hair without shampooing?

No, I think it just depends on where you are from, judging by the other responses. At "home" in NYC-It was always, can I get a wash and blow-out? or look at the way he blew out my hair :O lol...
But it is just as normal to say a wash and blow-dry..
When I get my hair blown out here in Portland, they blow it upside down first then use flat brushes ..I like my hair not being poofy but perhaps this style is just unlike what you have at home? (the South? South-West?)

I call it a blowout. Just an FYI. So do most salons in NYC, where I am from, and where I get blowouts on a weekly basis. That is all.

Maybe the term "blowout" is a Mid-Atlantic thing...it is used here in Philadelphia, too.

I'm originally from Staten Island and we always called it a blow-out. Now that I live in the South we just ask for big hair.

Being a hairstylist for 30 years, blowdry and blowout should mean the same thing to us...blowout doesn't mean big hair though, but the hand jestures and the word "volume" should have communicated that! She did what she wanted to do or what SHE felt was more in style.

I'm from Texas and we also use the term "blow out." That is how it is in all the magazines as well. Sorry you didn't get what you wanted! I'm a big volume fan myself!

"Blow Out" is also the name of a Bravo TV series about a tempermental LA salon owner.

FWIW.

In the middle of Canada we say blow dry. A blow out is what happens to a car tire when you are in your best clothes, with a fresh manicure late for a wedding.

Well, at least everyone seems to agree that the term 'blow-job' wouldn't be appropriate.

I've been living in Paris now for about 16 months and for a while I wondered which was was worse: getting your hair cut in French or going to the dentist in French. I speak reasonably good French but one day I was having a "bad French day" (i.e. not a day when the French are bad, which also happens, but a day when I can't seem to say anything correctly) at the hair salon - with a new stylist. The result was a nightmarishly short haircut - and the next day I had to fly home unexpectedly to attend a funeral. I looked like someone had just let me out of prison ...

Then, I had to find a dentist because I had broken a tooth. Ye gads - what is the French for "laughing gas", how do I say "stop that hurts", etc? It turns out that French dentists do not offer laughing gas. Oh, the horror. Actually, the experience turned out fine - thanks to Lexomil. (Perhaps I should take it when I go to the hairdresser.)

I concluded that it's worse to get your hair cut in French because you have to live with the all too visible results for a month or two if things go wrong.