yes, it sounds like you're not copying "ripping" the cd, just inserting and playing.
There are various tools to rip cd's:
Windows media player is ok, not great, but probably good enough for ripping cd's to MP3 or WMA.
Other players such as Jriver (the best), foobar, Mediamonkey, also have very good rippers (copiers)
EAC is the best of all cd copiers, open source and free (Exact Audio Copy)
Some cd's have copy protection. Windows media player will not bypass this protection (insert cd nothing happens), some other player/rippers may. EAC bypasses all copy protection. Also, Windows media player ripped cd's sometimes will not play on other than original ripped computer, i.e. other computer asks you to reinsert cd to acquire license.
You need to know what formats your car player will accept, and rip (copy) to one of those, probably only MP3, WMA and cda. If it's old, your only option may be to copy to cda format, follow instructions closely as this is copying old cd redbook format to same format different carrier i.e. usb stick or another cd.
If it sounds confusing, it's not. Any player / ripper, configured to rip (format, resolution, error checking on/off, folder location), upon insertion of cd pops up screen asking you to play or rip, sometimes both simultaneously. The issue of naming the cd, artists, album art, track names is another, extremely problematic issue.
