iBGP and eBGP peering can be run on the same router.

When BGP is used between autonomous systems (AS), the protocol is referred to as External BGP (EBGP). If a service provider is using BGP to exchange routes within an AS, then the protocol is referred to as Interior BGP (IBGP).

For instance:

Router A

router bgp 100

neighbor 2.2.2.2 remote-as 100 (this is an iBGP peer, same AS #)

neighbor 3.3.3.3 remote-as 200 (this is an eBGP peer, different AS #)

As for ASBR, this concept is used in OSPF to define a router that bring external routes into the OSPF domain.

For instance,

router ospf 1

redistribute connected subnets (the redistribute command will automatically classify this router as ASBR).

In an SP context, routers run eBGP to routers in other ASes to receive routes from these other ASes and they also run iBGP between routers in the same AS in order to exchange the external information originally received via eBGP.

The only router that is likely to run only iBGP is the route reflector, which is used to alleviate the need for a full mesh between all BGP routers in an AS.

Hope this helps,