ripping: music CD --> data on PC
burning: music data on PC --> music CD
The CD you received may contain MP3 files. MP3 files are data files and not recognized by standalone CD players.
You could copy the MP3 files to your hard disk, start nero, select audio CD (including 'finalize disc') and burn files as an Audio CD. This could mean that less files will fit, as Music CDs are burnt based on playing time, whereas MP3 files are burnt as data with a maximum data size (and MP3 files are compressed audio)