Wheel-ly Confused

I recently purchased a 2004 E320 4Matic Wagon. It's in great shape and mechanic says it's in solid shape. The tires are in need of replacement and the rims are rough, so I did some research on bolt patterns/sizes and picked up a set of W220 Wheels with wheels in good condition because I *THOUGHT* they matched the specs. But then I caught some others saying they aren't right. I'm confused by the charts I'm finding online - models numbers vs chassis numbers, etc.

Anybody give me some insight? Will W220 (that's a chassis number right?) wheels fit my E320 (that's a model number right?) Wagon?