Any time you see something like ___ chords, the blank tells you what part of a service those chords are being used in. So, shout chords are the chords you play while people are up shouting and praising God. They require the use of running a bass line in your LH while playing chords and runs in your RH.
Worship chords are the chords you play while people are worshipping God. These are usually soft and mellow chords. Any kind of slow song or progression played slowly and majestically will do here.
Phat chords is just another name for non-basic chords. These are your 9th, 11th, 13th, m7 (b5), etc. type chords. Any chord that contains more than 4 different notes is considered a phat chord here. Examples (not to be played in order, just random chords):
A / Db-G-B-Eb
C / A-Db-Eb-Ab
Eb / Gb-Db-F-Ab
Bb / G-A-C-D-F
Any other terms you having trouble understanding?