Instead of going into confusing details i will simply give a definiton for everyting related to filter that is commenly used

I will start with your main ones that you posted about
Sump : as the others posted a sump is basically a glass, acrylic, plastic, or fiber glass box that hold's filter media, pumps and the accessional protein skimmer
Canister: a canister filter is generally a box shaped filter that is under the tank or beside it like a sump but gerally there is more media, it is harder to see when media needs changing, and water gerally flows through all layers form top to bottom where it is then returned to the tank
"Rock": This would be live rock or sand that has beneficial invertebrates and organisms that help to control the "nitrate" cycle and alter wastes into forms that are easier to remove
Overflow: overflow is not a type of filter but a form of siphon that delivers water the filter
Protein Skimmer : a protein skimmer is quite simple to use but with a complex theory and process behind it so i will define it in a user friendly form. A protein skimmer is a form of filter that creates a torrent of bubbles which combine protiens and dissolved organics into the bubbels where they are then collected in a collection cup
"algae" : Algae is not a form of filter but it can be used as one because its potential is misunderstood. Algae as must of us here on the forum and in the hobby understand is terribly persistent because it needs very little. Algae is used in a refugium or a turf scrubber ( this is a complex filter that is used only for tanks with many thousands of gallons of water) to absorb nutrients from the tank to stop algae growth in the main tank. In theory algae is used to fight fire with fire or in this case algae with algae
"mud": I can see why this confuses so many people because mud is not really a filter but a filter media that is placed in a refugium to provide algae and microorganism with a home to live in and a place for these organisms to get main nutrients that they need.
Now i will explain the othor main filters and filter media
Power filters: power filter are some of the most commenly used and easist to maintain. It is simply a filter with and inlet and outlet and a filter pad with activated carbon in it
Activated carbon: This form of filter media is used to remove dissolved compound's but in a saltwater or reef aquarium remove nessacery nutrients and compounds that are need by the beneficial organisms so you have to be careful to get reef safe carbon
Bio-balls,ceramic rings,etc.: this filter media is used as a place for beneficial bacteria and organisms to live in
I hope this all helps and if you have any more questions feel free to ask!!
Wishing you the best of luck and a happy holiday
Firefish lover