Badges earned on per-site meta sites are separate from the main site, but reputation is carried over from the main site (because you don't earn any on Meta).
I perfectly understand keeping the rep the way it is (meta votes are too subjective to integrate them with rep) but the badge split seems odd to me.
Multiple badges are in fact impossible on Meta; Mortarboard, Bounty related badges. In addition badges in general are much harder to earn due to the lower amount of users and content; badges like Great Answer are nearly impossible.
As a result of this, most users on Meta end up with the easy 5-10 bronze badges for basic participation on Meta and not much else; stuff like Supporter and Critic that are hard not to get.
I understand the want to drive more people to meta, so perhaps badges are separate to institute a reward system; however this doesn't seem to work well since Meta badges (mostly) don't appear on the main site. This in combination of the 0 rep gain makes Meta feel almost not real. It also makes part of your progress (badges) on the main site invisible on Meta, and vise versa.
IMO the badges should be the same on both Meta and main site, but more Meta-oriented badges should be added to encourage use of Meta. This way Meta badges feel "real" instead of "Meta".
Is there an official reason for per site metas having separate badges?
[meta-tag:per-site-meta]
for that, but it's really not that helpful in this case since it's already linked in the list of tags below the question. That syntax is usually reserved for talking about the tag itself, putting it inline probably isn't necessary.