(Unfortunately I have a mix of SSDs in use, even in single personal computer, and all the vendor individual software gets overly complex and bloated...)
Better make sure the tool has a way to contact you if it finds an error! (Email by default - and test it!)
The long test reads the entire disk looking for errors.
Next, if you are using a Linux MD Raid array install mdadm and make sure it's configured to run a checkarray command (by default every month).
A short self test reads from random locations on the disk, it may or may not find anything, it's just a quick test.
Normally your hard disk will reallocate those bad sectors to other places, so you may not have any missing data, but once those bad sectors start they tend to keep going up. At some point your hard disk will run out of alternative places to store data.
But worse, any data in one of those bad locations is lost.
I would get your data off of the hard disk NOW. Then run a long self test and see if the numbers go up.
If your hard disk is still under warranty you should also go ahead and submit a claim.
Caveat: Some hard disks will create a bad sector if you power cycle it right in the middle of writing data. So a couple of those is not an indication of a problem. But 1,402 is rather a lot.
Post the full output of smartctl -a /dev/sda (or sdb, etc, whatever it is) and I can see if I can glean any other info for you.
[1] https://crystalmark.info/en/software/crystaldiskinfo/
Also relevant: https://ef.gy/statistics:ssd-write-endurance
On Windows there is Hard Drive Sentinel [1] and Diskovery [2]. Crystal Disk Info is a hit-and-miss, it's too prone to misinterpreting attributes and showing nonsense.