What's the difference between a LM3302N, TLC373CP, and LT1101CN8?
The LM3302 is a quad equivalent of the dual LM393. These are very popular 'industry standard' comparators made with bipolar transistors. Robust, work on a wide range of supply voltages, cheap, and have been around forever. If a device needs several comparators and the application isn't too demanding, chances are one of these will be in it.  

One useful feature of the LM3302 is that the inputs work down to 0V on a single supply voltage, which makes it suitable for devices that only have a +5V supply. 

The LT1011 is described as "a general purpose comparator with significantly better input characteristics than the LM111." which "retains all the versatile features of the LM111". In other words it's an enhanced spec version of the LM111. Its balance/strobe pins make it more accurate and versatile than the comparators in the LM393, but the extra pins limit it to one comparator per 8 pin package. Its inputs cannot go down to ground unless a split power supply is used.  

The TLC372 is a CMOS replacement for the LM393. Its main advantage over the others is extremely high input impedance and negligible bias current.  


  I think they would all work as long as I don’t exceed 20mA and LT1011
  is confusing me with it’s title “voltage comparator.”


The LT1011 is specified for up to 50mA output, but the LM3302 and TLC372 are only guaranteed to sink 6mA ('typical' output current is 16mA at 1.5V).

They are all voltage comparators. A voltage comparator is similar to an op amp except that it is designed to run open loop for producing digital output, rather than with feedback for linear amplification.  

Some op amps compare current instead of voltage. The LM3900 is an example. Current-mode amplifiers can work at higher frequency, but have low input impedance.