distance??

How did you measure the distances? If the golf shop uses a computer to calculate distance then it could be set wrong. Also differences in temperature between golf shop and outdoors would have an affect. Different balls. Lots of variables...

I only know my own experience, but if you hit it a little fat on a mat, it doesn't cost much distance, but a little fat on grass does. I fooled myself into thinking I was making a lot of progress based on my hitting off of mats. I had to just get a lesson again so I could learn to hit of grass again and lose some of the bad habits that snuck in.  It got so bad I couldn't even hardly swing at a ball on grass. The pro walked through some video analysis with me and made a couple of adjustments to my swing, and zowie.

Same deal with practice swings without the ball as an exercise. They can screw you up too. I was using a Slice Eliminator, which is a good product, to learn to swing inside to out, but without the ball. I did like 50 swings a day, 10 at a time in my back yard, for a few weeks. (I work from my house.) My slice went away, but my contact became really erratic.

Same thing, part of my swing had rotted away from getting bad feedback. Now if I do hit off of mats, I try to be really aware when I hit it fat. I might lose ten yards off of a nine iron, but I have to know that that will be 25 or thirty yards on the course.

See @Moppy 's response. . .

10 yards easily. . .

This is perhaps a stupid question, but you were using your own 7 iron in the shop and not some other demo 7 iron, right? Asking just in case it's that simple, haha.

But yeah, any combination of real world conditions of wind / denser air / cold balls, hitting it fat, or miscalculated real world distances could account for part or all of the discrepancy. Next time you're hitting on grass, mark the ball position with a tee a few inches off to the side and note whether your divot is before or after the tee after you hit the ball. If it's before, there's your answer. If it's after, check what your distance was and, if it's still less, start ruling other things like wind, elevation, etc. out.

Hitting off a mat is generally be farther and more consistent than off grass. It also hurts the wrists more if you are hitting down enough on the clubs.

Both of those statements depend really heavily on the kind of mat and what kind of strike you're making, even though I wouldn't really quibble with the consistency point too much.

I should have qualified that with "from my experience" at our local driving ranges. . .and I take deep (probably too deep divots). Something I'm still working on. . .

Yeah, totally, fair enough. I personally have gravitated to one range that has really thick and soft mats that help with both better feedback and being good on the wrists, haha. If I were still going to the ones that were barely more than astroturf on concrete, you'd get no argument from me!

There's one range where they have that thick fluffy replaceable grass-like inserts, so I kind of know what you mean. However, I think I'll just practice on the course whenever I can. That seemed to give me the best results anyway. . .I'll just have to find days when there are not as many golfers on the course.

Or get more swing keys (5SK). Working for me. . .

I generally hit it farther on the course than at the simulator because most simulators are set to sea level and I play about sea level and the air is thinner so ball travels farther.  But could vary on a case by case basis. The best thing is to find a field or place to hit balls where you can walk out to where they land and then hit balls with the same club(s) then you can really see the true distance and get a good feel for your "clusters" so to speak.

Were those carry distances? Only trust carry distances from golf shops, and even then, don't trust them unless you can compare your current clubs.