Both use electrical resonance to create a magnetic field to move a pointer, differing in their exact construction.
The BTH meter, named for the British Thomson-Houston heavy industrial firm, consists of a magnet coil connected to the input signal.
Running through the center of the magnet is an iron core which extends past the end of the coil and is curved and tapered roughly like a sabre.
This moving coil is connected to a capacitor to produce an LC circuit tuned to a particular frequency.
Two such paired coils are used, arranged at right angles so that the resulting assembly looks like a hash mark, #, when viewed from the side.
For radio frequency signals, these systems were generally far too slow to react, and new meters were introduced.
The absorption wavemeter is a simple system consisting of a single tunable LC circuit and a separate voltmeter or ammeter.
The two signals mix and an audible "whaa-whaa" or "beating" can be heard at a much lower frequency, often a few Hertz.
The piano string is then adjusted until the beating disappears, meaning the two frequencies are (close to) equal.
The user can then change the frequency of their LO radio until the audible signal disappears, in same fashion as tuning a piano.