MPLS L3 VPN means the service provider participates in customer routing. For example, take a look at these lessons:
For a high level overview, take a look at this lesson:
Between the PE (provider) and CE (customer) routers we run a routing protocol like OSPF, EIGRP, RIP, or BGP.
With MPLS L2 VPN, we don’t do routing between the PE and CE routers. We transport a L2 protocol like Ethernet or frame-relay, over the MPLS network. To the customer, the MPLS network is transparent and to them, it seems like a regular L2 link. Here is an example:
I hope this helps!