Wobbly wheel - spokes or bearings
If you spin the wheel by hand with the bike off the ground, then side-to-side wobble is also called "out of true" and is caused by spoke tension, or an impact while riding.  Wheel going badly out of true on final tightening 

On the other hand, if you hold the non-spinning rim in your hand and move it left/right while mounted in the bike, there should be no play discernible or visible at the axle.  If you feel motion sideways, then its bearings malajusted. How do I know if my cone/cap/bearings need to be adjusted?

A wheel can have both, or ideally neither, or either.