Anything used for internal Android usage will be formatted completely differently from the standard FAT32/exFAT, which is most likely what's going on. It it wasn't detecting the SD card it probably wouldn't ask you to format it.
A reader from 2011 is almost certainly SDHC (spec from 2006) compatible and likely also SDXC (2009) compatible. Also I vaguely remember something about being able use bigger cards on older readers in an out-of-spec sort of way some situations.
Edit: Also looked this up SDHC readers can read/write SDXC cards, only slower it seems. And I think what I remember was that 4 GB cards worked in many devices that only supported OG SD standard, which was only 2 GB.