I've used the KMC Z72 chain on 2 of my bikes and they work well. My local bike
shop tell that chain has been replaced with a KMC 8.1 chain,They also havean
8.3 chain along with others. Is there any difference in all these chains that are
made for 6-8 speed bikes?

I've switched to 8 speed chains on all my 6 and 7 speed bikes. I think I even have one on a 5 speed freewheel. It came off a bike I switched to 9 speed.

Z-series and X-series KMC chains are two very different quality levels.
Z-series works well, is very low-priced and is reliable, but has very loose tolerances for pitch from one link to another, so much that I have a hard time determining the exact level of wear using any of various measuring tools that references off of the rollers. Perhaps it's just the rollers that aren't concentric, more likely the overall mass-produced construction(?).
At any rate, I hesitate to use the Z-series chain on my more-prized freewheels for harder and higher-mileage use.

X-series on the other hand is race-quality chain with much better tolerances, higher tensile strength and higher pin-retention force. So it costs a few dollars more. Definitely on par with comparably-priced chains and seemingly better value than most.

I will need to see how the new model names compare to the old names. I just bought some KMC 11s chains in the new packaging but their was no doubt that these were of the high-quality grade since I don't think they even make a cheap-QUALITY 11s chain.

7.1 and 7.3 refer to the pin width, and is the outside measurement of the chain. Shimano HG is 7.3mm, SRAM is 7.1mm (these are all 6-7-8s chains).

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...I used to use the Z series chains, but once the X8 series started selling on places like Amazon for less than 50 bucks ffor five of them in a bulk package, that's all I've used in the past 6-8 years. They work well on everything I have, and that covers a broad range of stuff, from the 60's up to the 90's, with 8 or fewer cogs in back. I think they still make and sell the Z chains, but I don't know why anyone would use them instead of the X plate ones.

The wider z-series will shift better on some low-level double chain sets. And they're probably a little cheaper if you need just one.

There seems to be a dizzying array of KMC chains. I think the OP can only trust the bike shop here. In most cases you can identify the fancier X series by the fancy shape embossed on the outer plates.

I used a KMC 8.99 for a while. Worked well and looked nice. Didn't last that long compared to some other chains. It didn't 'stretch' particularly fast, but the rollers were all getting pitted after 3k miles or so, a little bit prematurely IMO. It was kind of strange. That's not an unreasonable lifespan I suppose, for a relatively inexpensive chain.

I use KMC X8.93 or X8.99 on most of my 6/7/8 speed builds. I’m a fan. Difference between the two is 8.93 is silver and black while 8.99 is all silver.

That must be the one with the flat outer plates(?).

I have Z51 in the box here that measures 7.15mm and the box says 7.1mm width.

I really liked the older z nickel plate chain but ounce KMC switched production on these to China a couple of years ago I found the z chains not so good. Switched to the X8 and found these to be the best chain for under $25.
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The KMC Z-72 was the best of that bunch of older style KMC chains, with outer plates shaped for crisp shifting, mushroom head rivets, a Missing Link, and good wear qualities for an inexpensive chain. I usually bought 'em via Amazon for around $7 each, and still have a few. No problems with my various 7-speed setups, using Suntour and Shimano groups, freewheels and cassettes.

That particular chain worked best for me with index shifting. The shaped plates could be a bit fiddly with friction shifting and I found myself fine tuning the levers more often than with the cheaper Z51 and similar chains with flat plates and plain rivets, particularly with Suntour Alpha freewheels. Not sure why. I've switched to all SunRace freewheels because they shift and run better (but only the MFR-30 and MFM-30 chromed 7-speed; not all SunRace freewheels are made as well).

I noticed KMC revamped its lineup, mostly renaming some existing chains, but also apparently phasing out others. So I've stocked up on a few Shimano and SRAM chains to try, since REI was blowing out some parts cheaply this summer. Good time to stock up on older style drivetrain bits because the pandemic is disrupting the supply chain and some stores may not restock these anytime soon.

Yup, shortages and price increases on everything. I put a favorite topical analgesic into my Amazon cart a few days ago when it was $19, the usual price for the past couple of years. By the time I went to confirm the purchase after shopping for a few more items, the price went up to $24.

I put a bunch of stuff in my Amazon cart, then move it to "save for later." I check it often for price drops and buy it immediately.

Last year I bought a pair of Continental Grand Prix Classic skinwalls for about $30 each. Rode 'em for a year, decided they're keepers, and might turn out to be my main road bike tires. But when I checked prices a month or so ago they'd gone up to $45 each. I put 'em in my Amazon save for later cart and when the price dropped to $35 I bought 'em again.

Since then not only have prices increased, but USPS deliveries have been hobbled and everything is much slower now. All of my mailed prescriptions are running late and some have been cancelled and scheduled for re-delivery.

If you need something now or anticipate needing it during the next year, buy it now. I suspect things are gonna get worse.

I still have 4 of the SRAM PC 890 chains because I bought 10 of them before they were discontinued. Most of my bikes are 6 or 8 speed and the chain works well. Even used one on a 3/32 fixed set up.

I like the PC 890 also for friction or 3/32 SS/FG setups the straiter simpler plates seem to work better for those setups.

I have SRAM PC 890 on just about all of my 6/7/8 speed bikes.