Ok ok ok. Let's clarify this in the most basic and straight forward way possible, by literally listing each scanner in the game with its proper name and a functional discription, and then then you can go forward with the proper presumption that anything not listed here is incorrect if it's from any other source.
To start with, there are 3 scanners built into every ship, which appear on the internal systems list on the right hand panel. These scanners are named thus;
Composition scanner
Data link scanner
Discovery scanner
The composition scanner is used for scanning things like biological and geological sources in the game. Fumaroles, geysers, brain trees, that kind of thing. It's name is pretty apparent, in that it scans the composition of things, ie, their make up and structure of objects and entities.
The data link scanner is used for scanning data sources, as its name implies. Probes, mainframes, computer systems, guardian technology, etc. Anything that is a computer which can be interfaced with, use this one.
The Discovery scanner is the one you seem most confused about, and which you have listed multiple times on your first list. It used to come in different forms, and acted as any other module you could buy, with different sizes/classes. Now there's just one. This is the scanner you use to initially find stars within a system. Colloquially known as the "honk" for the distinctive sound it makes upon use. Essentially it acts like a sonar ping, to initially locate large bodies.
Now, this is where things get a little more confusing, as, related to the Discovery Scanner, there is another scanner called the FSS, or the Full Spectrum System. This one does not appear in your modules list, but, like the others, is also built into every ship as standard. In a way, it is an extension of the Discovery scanner (or the discovery scanner is a part of the FSS, if you want to look at it that way). By using the Discovery scanner within a system, you basically "unlock" the ability to then perform a FSS scan. You cannot use the FSS without first using the Discovery scanner (or honking, as we call it). With the FSS, one can locate all planetary bodies within a system, by panning around and zooming in on individual signal sources. It is the primary way one finds planets in the game.
All of these things mentioned above are the correct terms and definitions of the systems built into each and every ship. Learn them. Know them. Use them. They are what they are and are used as described.
There are of course, various other scanners in the game as well, all of which are modules that must be bought. They are;
Detailed Surface scanner
Pulse wave analyzer
Frame shift wake scanner
Kill warrant scanner
Manifest scanner
AX Xeno scanner
Of these, the Detailed Surface scanner (or DSS, for short) is a module that allows one to fire probes at a planet in order to map their surfaces. Mapping a planet increases the money you earn from selling cartographical data and puts the "First Mapped by ..." tag on the planet with you name, in the case of any planet not previously mapped. It is of extreme value to explorers, as this is the module that generates the most revenue for those in that trade.
The pulse wave analyzer (or PWA, for short) is used for mining (I assume this is what you meant by "mining scanner" in your first post), specifically for finding motherlode asteroids that can be blown apart with seismic charges. I believe it is currently bugged, and has yet to be fixed, but when working it shows asteroids within planetary rings as various hues of red and yellow, for identification of the minerals within.
The frame shift wake scanner (or just wake scanner, for short) is used to scan wakes, ie, the leftover energy that ships leave behind when they jump either to supercruise or to hyperspace. They can be used to track ships from one system to another for bounty hunting, but more often they are just used to acquire certain forms of data used to engineer ships.
The kill warrant scanner (abbreviated to KWS, for short) is also used in bounty hunting. It allows you to see additional bounties that may be placed on a ship, from sources outside of the current system. Normally you can only see bounties that have been accrued within that same system, so these additional bounties are hidden and can only be revealed by use of a KWS.
Manifest scanners (no abbreviation) are used by pirates to scan the cargo bays of target ships. That's really all that can be said on that one, I think it pretty much speaks for itself really. It scans the cargo manifest.
AX Xeno scanner is for scanning aliens, mostly Thargoids. Again, it's pretty self explanatory. It scans aliens. Nuff said.
These are the correct terms for the scanners that currently exist in the game and a basic overview of their functions. Any other terms are incorrect. If you wish for more information or don't beleive me, then check the wiki and do some more reading on there. If you're still confused even after this, then, IDFK man!
The wiki page