Yes, ground loop noise is "common mode". Balanced mode rejects common-mode noise, either induced our coupled from the outside environment or impressed on the line because of a difference in ground potential. The fact that your balanced input doesn't reject it indicates one of two conditions: the balanced input has a limited common-mode rejection ratio (yes, you can have a balanced input with poor CMRR, it's done all the time, and CMRR is almost never included in the specifications!), or the noise is not common-mode (unlikely). That would be common-mode noise. Good CMRR is greater than 70dB, hopefully. There are many variations on design, and many suffer from poor CMRR under certain conditions, such as an imbalance in source impedance. Here's a link to a good monolithic solution, a THAT 1200. It is an expensive part, and not typically used in consumer applications. Note the data about CMRR under a condition of imbalanced source resistance, and note too that CMRR is not flat across the entire audio band. This is very typical, and the THAT 1200 solves the problem mostly. Less expensive designs use a simple differential input with terrible CMRR and intolerance to impedance imbalances, or they use a conventional instrumentation amp configuration, better, but still can have issues if not properly done. A good balanced line receiver will have 90dB CMRR across the audio band, a bad design might hit 60dB at 60Hz, then collapse to 10dB mid-band and up. There are also maximum voltage limits to a devices CMRR, which is one of the advantages of using a transformer as a balanced line interface. That and complete isolation.