I think most of us think of a "truly balanced amp" as having three properties all of which reduce crosstalk:
1. Balanced input meaning identical impedance in the positive and negative inputs (so common ground between the left and right channels cannot be used).
2. Balanced amplification meaning complete separation between left and right channels so no common ground in the amplifier circuitry (dual differential or push-pull amplification is normally used).
3. Balanced output meaning balanced (identical) impedance in the positive and negative transmission lines (so common ground cannot be used). The primary benefit of balanced output is to take advantage of common mode noise cancellation.
Each of the 3 can be implemented independently:
An amp can have unbalanced (common ground) input with balanced push-pull amplification with balanced or unbalanced output.
Some amps have balanced input with ground referenced single-ended amplification with balanced output.
The schematic below shows a single-ended amp with balanced output. The KT88 is definitely being used as a single-ended amp but the speaker side of the output transformer is not grounded so it acts as a fully balanced output and would offer matching impedance on the + and - speaker outputs so it would offer common mode noise cancellation. (But if you used a coax for speaker wire and wired the + to the center conductor and the - to the shield you would lose common mode noise cancellation due to conductor impedance mismatch. The coax has unbalanced impedance.)
Here's a push-pull amp with common ground (unbalanced) output. Note the ground symbol on the speaker tap at far right:
In layman's terms, the opposite of push-pull is single-ended and describes amplification circuitry. The opposite of balanced is unbalanced (or common ground or single-ended). It's used to describe how circuits or components are connected.
Edited by robrob - 12/30/13 at 12:23pm