Assuming that they aren't simply lying(sometimes a safe assumption...sometimes not so much) "Class 2", "Class 4", "Class 6", and "Class 10" are supposed to be guarantees of 2, 4, 6, and 10 MB/s minimum write speed, respectively, while UHS1 is supposed to be 10MB/s with support for UHS bus operation, and U3 is supposed to be 30MB/s with support for UHS-II bus operation.
How they store bits, internally, is not specified; but minimum write speed is obviously fairly important to people shooting video or enough large still images, quickly enough, that dumping them to flash can be a bottleneck. Unfortunately, despite the increasingly common case of SD/MMC-bus connected devices being used in situations where read performance matters as well(eg. storing programs in cellphones, being rPi root filesystems) standards for testing and labeling read speed, random I/O performance, and similar SSD-enthusiast stats are more or less nonexistent.
As bulk storage for music files, a Class 4 is likely to do just fine( even golden-ears FLAC is what, 5-6 megabytes/minute?); but unless the stickers are pure lies, a Class 10 is likely to be a rather nicer card.