There are many different types of LMEs (Liquid Malt Extract is the term we use) processed by a handful of malting houses around the world. There are pure versions of it, made with a single grain, as well as some that are blended from various types of grains that were processed differently to produce different colors and flavors.
And every maltser's extract will indeed taste different.
Also LME is categorized usually by color, from Light to dark, and these differ in flavors from very light malt flavor all the way to those having a burnt caramel/roasted coffee/nut/chocolate notes to it.
The barley malt syrup from the health food stores IS the same thing as we use, EXCEPT it tends only to come in one color grade. Additionally my understanding is the stuff in a health food stores tends to be of a lesser quality that what we use. Basically a maltser will use some of the lesser quality extract for the health food and baking industry- Flaws would be more noticeable in beers than foods or adjunct sweeteners in coffee.
Additionally some LME comes pre-hopperd. And even during prohibition it was sold to be used (supposedly) for baking, there were even cook books sold that called for hopped LME.
There's way too many blends and versions and grades to narrow down. You'll need specifics, there should be a name on the stuff your bakery...It's a food ingredient afterall and therefore regulated, so the container SHOULD be labeled, and it should say the type, and who made it or who distributed it. THEN we can nail it down...but not with such scant information.
One of the most "famous" malt extracts used in the baking industry is from Premier Malt Products, which used to be "Blue Ribbon Malt Extract" which if you're familiar with Pabst Blue Ribbon Beer- it's the extract that they brewery made and sold to stay alive during prohibition. They are located in Michigan and their website is here.
They produced a cookbook back then-
There's a good possibility that the bakery uses theirs even if they got it through a brewer's supply house.
But they should be able to tell you what labelling is on their containers, or a shipping or ordering manifest from them should give you some more info.
If you give us some more info we might be able to help. But their are literally hundreds of types of LMEs out there. Some brwer's supply stores buy various pure grades and custom blend for their beer kits. So narrowing it down with no info is going to be nigh impossible.
If you can find more clues, feel free to post in here, or private message me and Ill see what I can do to help.