The values on the left and right can be two different things. Either the measured value for each half of a dual-triode tube, or sometimes it is the measured value in the numerator over the expected NOS value in the denominator. For example, a tube that tests 1500/2000 will be 75% of nominal value, if the seller is listing it as a fraction. You can always ask the seller.
Correct, you are most commonly going to find three different value ranges, although there can be more.
Numbers like you listed above are likely a measurement of a tubes transconductance. Tube testers that test transconductance are the most advanced and test the tube most similarly to how it would be used in a circuit. The nominal value will be specific to the tube under test, check the tester's manual for minimum expected value or the tube datasheet (manual is better since transconductance is not truly constant and the tester will use specific test parameters). The Amplitrex AT1000 electronic tester is the Rolls Royce of testers, it will give mutual conductance and plate current values.
Another type of value you will see might be in the 40-80 range. These are the TV7 type Hickok transconductance testers. They test a tube like above, but use their own normalized range of "good" values. NOS tubes tested by a TV7 will have a value around 70, you can check the TV7 manual for tube specifics.
Lastly, you will often see percentages listed, "95%" or "110%". These are emission testers, they test a tube's cathode emission by basically operating the tube as a diode with a specific plate voltage. Not as telling as a transconductance tester, but will give you an idea of the tube's usability and remaining lifespan.
There are other oddball testers used out there, but these are the most common values you will see on eBay. None of it is standardized.