This is a 'How long is a piece of string?' question.
6000 MP3's will take up a different size to 6000 AAC's or 6000 Apple lossless files and the same is true of 6000 WAV or AIFF files (the audio CD format).
Also consider that every song can be any length from a few seconds to many minutes or even hours for some performances. The sizes that Apple quote will normally have some incredibly fine print disclaimers, search the page for some tiny grey text if you want to see the caveats that Apple list or check the box/ packaging.
If you cannot fit all your songs onto a device you have a few options…
- Re-encode the songs to a more compressed format (basically set the 'import' format in the iTunes Preferences & then ask iTunes to convert to the [chosen format]).
- Allow iTunes to re-encode the files over a certain size - this is normally setup in the sync settings - select your device in iTunes & edit the Summary section, enable 'Convert higher bit rate songs to …'
6000 of my songs selected at random seems to be about 51GB that plays for around 22 days, I have quite random formats & bit rates etc.
I think 'a fair few thousand songs' is an appropriate term for that quantity of music, what is is specifically that bothers you?
You will need to use 'File > Get info…' in iTunes on some of your songs to see if you have high quality formats or just files that are uncompressed, that may explain why you are able to store less items.