Alkalinity = Carbonate Hardness = KH (note that alkalinity ISN'T alkaline)
Put to simple terms, this is the level of resistance (level of carbonate and bicarbonate) the water against changes of
pH.
Go a little bit deeper. The end results of the
nitrogen cycle is
nitrate, which is also called NITRIC ACID, and we all know that acid lowers the pH, sufficient about of KH would neutralize these acids and they would not cause pH swings.
To raise KH, simply add sodium bicarbonate in correct amount and aerate the water (less CO2, more KH)
General Hardness (not-too important)
Balance of
calcium ions,
magnesium ions, and other ions in the aquarium. These ions are needed for internal functions of fish but almost never need to modify or worry about as there are always sufficient amount in a good aquarium, unless it comes to breeding certain fish
To raise GH add coral to filter, to lower it add peat moss or use RO water.
TDS (Total Dissolved Solids)
The TDS meter measures EVERYTHING that has dissolved in the aquarium that isn't pure H2O molecules, that literally means everything. This includes from simple
chlorine, phosphorous, nitrates, oxygen, carbon dioxide to complex compounds of dissolved organic compounds. Every single thing that you add into aquarium water will raises TDS level, stuffs like Prime, water conditioners are included

.
It's pretty awesome little machine really (very affordable too), I stick it in distilled water I get 0ppm as its meant to be, tap water ~30ppm, aquarium water ~75ppm and freaking cocacola 600ppm (look all the sugars and stuffs in there). And amazing Diet Coke isn't all that different, I bet they replaced sugar with a bunch of other chemicals. Sorry for the off topics.
Overall, TDS meter, KH
test kit and GH test kit measures very different things and none of which can replace another.
PS: Sorry for the essay, except going off topics I can't get any simpler yet staying informative
