Different polar patterns not only dictate how directional a mic is, they also have different frequency responses, resulting in different sounds.
Cardioid mics have what’s called a unidirectional pickup pattern, which means they are good for isolating the singer or instrument being miked up. Their pickup pattern faces a single direction.
Omni-directional mics pick up sound from all around, but their character is more open, natural and less nasal than cardioids. Omnis also suffer less from the proximity effect - the low-frequency boost that appears when close miking.
Bi-directional mics, more commonly known as the ‘figure of eight’ pattern are sensitive to sound from the front and back, but reject sound from the sides. These aren’t the most popular but they can be useful for picking up two different sources positioned side-by-side.
So, although it seems logical to reach for a cardioid when miking up a vocalist, you may be better off using an omni in a well-treated room where reflections have been minimised. This could be an expensive studio or a spare bedroom with judicious placement of duvets and blankets!