Microphones that respond exclusively to sound pressure are inherently omnidirectional. Microphones that respond exclusively to sound velocity are inherently bidirectional. Most microphones use a mixture of the two principles. If you have a microphone that gets half its sensitivity from pressure actuation and half from pressure gradient (=velocity) actuation, the result is a cardioid. A hypercardioid pattern would result from a specific mixture that is nearly all pressure gradient.
Not very many actual hypercardioid microphones are made; patterns between hyper- and supercardioid are much more common (what the various manufacturers call the microphones in this part of the spectrum isn't usually very exact). Also, unfortunately, on this board and elsewhere some people call shotgun microphones "hypers," which is incorrect and confusing. If you're really asking about shotgun microphones please say so, because otherwise the answers you get are likely to mislead you.
The sonic difference between two cardioids of different design may well be greater than the sonic difference between a given cardioid and a super- or hypercardioid when the two mikes are designed as part of the same family. Directivity is one thing while the frequency response is another, and often those two fundamental attributes of a microphone depend on one another, i.e. with many microphones (particularly the more affordable ones) the frequency response may vary depending on the angle of sound arrival--or to put it another way, a microphone may be a cardioid at 1 kHz but at 100 Hz and below it may be closer to an omni or a so-called "wide cardioid" while at high frequencies, it may have a narrower pattern.
To be continued ...