A proportional counter is built the same way as a Geiger counter, but uses a lower high voltage: Any incoming ionizing particle ionizes the counting gas inside and so allows for a current to flow between the two high voltage electrodes (a metal wire in the middle of a metal can). Now, for a Geiger counter the voltage is so high that the electrons that the particle seperated from the gas atoms are accelerated so strongly that they knock off other electrons from their atoms which in turn do the same etc., ending in an avalanche, so that every particle, even with small energy, gives rise to a high current which is easily detectable, but largely independent of the particles energy.
However, if the voltage is lower, no avalanche is formed. Instead, only those electrons and ions produced by the particle itself are drawn to the electrodes. By measuring the total charge (time integral of the electric current) between the electrodes, we can find out the particles kinetic energy — because the number of electron/ion pairs produced by a travesing particle is dependent of its energy, and —if the voltage is chosen right— actually proportinal to it.
Hence, if you lower the voltage of a Geiger counter to the proportinality range and fit it with a sensitive amplifier and a charge integrator, you get a proportional counter. On the other hand, most proportional counters can be switched into "Geiger mode", i.e. the voltage is increased to get an avalanche and make the device work as Geiger counter.