In a most general sense:
Basically (in most but not all cases) a balanced antenna is one where the elements are fed and are of equal length on both sides such as a dipole antenna. Balanced antennas can be fed with open wire transmission line or with coax with a Balun. One of the exceptions is the OCF dipole. It is one of those antennas that has the balance feed point shifted away from the center. A dipole has a nominal impedance value of 73 ohm (it can be fed with 75 ohm balanced line, directly with 75 ohm/50 ohm coax or with cox and a 1:1 Balun), but when the fed point is shifted away from the middle the impedance value starts going up. The 14% point is somewhere between 300 and 200 ohms, which is why you will see some use a 4:1 Balun or a 6:1 Balun.
Whereas an unbalanced antenna has one element being fed such as a ground plane, or a coaxial dipole. A HF vertical antenna using radials is definitely an unbalanced antenna and can be fed directly with coax or through a 1:1 Unun. Many multi-band vertical antennas will be fed with a 4:1 Unun to help the antenna tuner find a low impedance point over a wide frequency range.
If you go through the ARRL Antenna Handbooks, or most any other antenna handbooks you will generally find the same results/conclusions.