Well, let's see: You have 'totally customized', 'partially customized' and 'totally custom made' and 'partially custom made'.
I would think the first is a mass produced firearm completely worked over with all parts replaced, with the second having only some parts replaced. The third is completely hand-made or hand-completed from worked over mass produced parts (Mauser actions, e.g) with the other parts being custom made (barrel) or custom engraved (floorplates, etc.) and the fourth would be a partial version of the third.
Now, this is jmtcw but I have two Winchester 94 AEs that I consider custom or customized yet they started life as factory made mass produced, as were my Swedisha Mausers and my sproterized mil-surps.
I agree with Rangr44 that a customized rifle is a inexpensive shortcut for someone who may not be able to afford a truly custom rifle. Thankfully this does not mean that the customized rifle amounts to anything less than the truly custom rifle and all my customized rifles shoot as well as if not better than some truly custom pieces I have seen.
When I see someone come to my range with a truly custom rifle I always compliment him on his fine or sharp lookin' rifle-gun and let him talk it up. I never verbally compete with someone who has spent the $ for a custom piece, and I may even spot for him when he shoots. I never criticize anyone's concept of artwork, I simply allow them to make their own comparisons after I have shot my rifle...........and that's how it goes.......