Balanced vs Differential

Balanced requires balanced impedance on the two signal lines. For a balanced output, you could send your AC signal on + and 0V on - and as long as the impedances are matched between + and - outputs, you would have an impedance balanced circuit. Some call that pseudo-balanced output, compared to a differential output with balanced impedances.

Differential does not require balanced impedance. "Current feedback" amplifiers have differential inputs, one of which is a typical high impedance input, while the second presents a low impedance. A single transistor (singleton) input stage would be an example, with a high impedance input at the base and a low impedance input at the emitter.
 
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There are several kinds of balanced - balanced impedance (source or load or both), balanced signals (common-mode is zero). Differential just means the signal is the difference of two wires, neither of which is ground.

There's even a mode where the receiver drives the cold wire (to local ground) and the transmitter adds that to the signal to define the hot wire - definitely differential, but not balanced in any sense.
 
They are one and the same.
Not true. Balanced implies Transformer balanced on both the send and recieve side in locked loop transmission.

Differential or Electronic Balance is the cheaper, lower performance, lower compatability transformerless option. I have devoted much of my life to this matter. True balance is better in every possible measureable way.

Edit. Balanced transmission is a power curve. Differential inputs measure voltage, often in an overly expanded and erratic mechanism that does not actually reference a current limitation. You take the differential voltage and dump it into the speaker you dont hear the motion of the capsule, you hear overshoot flyback and capsule rattling/distortion. The voltage doesnt mean anything except it has transformable information in it. A speaker will move more efficiently when powered by a precurved signal such as one that was transformer matched at its souce, and ideally at each node in the chain.