Hi! As a huuuge sheet mask enthusiast, I had to chime in! The difference I find between clay masks (and other types of mask that you wash off) and sheet masks is that the wash-off masks tend to be more cleansing (clay masks especially are targeted towards helping draw out impurities from your skin) whereas sheet masks are more for hydration/treatment. There are an infinite number of types of sheet masks, but what you'll find is they all tend to target some sort of area or cite a certain treatment - "good for redness", "good for hydration", "good for troubled spots (anti-acne)", "good for brightening (dull skin)", etc. Sheet masks are essentially serums that are left on your face to be soaked and absorbed for a while (around 10-20 minutes are stated on most instructions, but there's no harm in leaving them on for longer - I like to keep them on until the mask is almost dry, and I also swipe the excess onto my neck/décolletage). I would not say sheet masks are necessary, but they are a fun little luxury at home for when you want to pamper yourself. I know that some other sheet mask enthusiasts would disagree and say that sheet masks are an absolute necessity to their skincare routine - they would do some every day, some even twice a day (morning/before bedtime). I personally try to do it once a day just because I enjoy the process, but in reality I do it only every few days.
If you're interested in trying sheet masks, I would suggest you stick to the Asian brands (Korean specifically). They are the original and frankly the best bang for your buck, as well as simply the best in performance. Of course, each person will have their favorites among the Korean brands as well, and that's just something you'll have to see for yourself after trying a few. Also I had to mention the price discrepancies between the eastern and western brands because I cringe when I see the Sephora sheet masks that go for $6 when often you can buy a set of 10 Korean sheet masks for about $10-$15, depending on the brand and type. The western brands are currently hopping on sheet masks as a 'trend', hover they are simply staples/a normal part of many Asian (particularly Korean and Japanese) skincare routines, and will continue to be even if/once this 'trend' passes.
Anyway, I hope you give them a try! Let me know if you need other resources to do research before trying out a few, if you are interested!