As GTB says - the Mix and the Mastering are 2 very different processes. During the mix you will apply the plugins (EQ/Compression etc) on individual channels and instruments. Mastering plugins will be applied to the (Master ) Stereo Output (or surround outputs). In its most basic form mastering will consist of EQ and Compression?Limiting as well - but because it's applied to the "Mix" bus the plugins will affect everything in the mix equally - but that's what mastering is about. Let's say overall your mix is great but when you check it on other speakers it sounds "dull" - then you might want to dial in some more top end using an EQ plugin. You will also probably want to actually reduce the dynamic range - which in effect will make the track sound louder overall - it will also help to "glue" the mix together more. Please understand I am simplifying massively here... You might also want to apply other dynamic effects such as limiting - or enhance the stereo width of the final mix.
In terms of which actual plugins to use - although in essence they are the same as for mixing, in reality there are many plugins which are far better suited to mastering, or even designed specifically for mastering. For instance, you would probably use a multiband compressor for mastering rather than a single band one. Equally you may well use a linear phase EQ rather than a simple channel EQ, but the priciples are the same. Logic has all of these built in - but I don't know any mastering engineer who uses them. Some of my favourites would be Waves LinMB, LinEQ and L2, Slate FG-X, UAD Precision Range and Manley Massive Passive. Alternatively you could just bounce the stereo file out of logic and then use something like Ozone or T-Racks.
I would just add that while mastering is in theory a separate task from mixing, performed afterwards - sometimes, particularly with todays super loud mixes, it can help to have some basic mastering style plugs on your mix bus as you near completion of your mix so that you can hear the effect the mastering process will have on your mix. BUT - don't put them on to early, otherwise you'll get the mix wrong, and turn them off once in a while to check what the mix sounds like. I sometimes bounce a rough mix with them on (in Logic) so the client can hear what the track will sound like and it's nice and loud - but once the mix is approved I will always bounce the mix with them turned off and master in another program - not because you can't do it in Logic - it's just a work flow thing for me and I end up with better results (though technically there is not necesserily a reason why this should be so)
Hope this helps... If in doubt - send your track to be mastered - it's so cheap these days there's really no reason not to...