Areas, ABRs and ASBRs: know your borders
The backbone, an area border and an external route are three different ideas. Here is how they fit together.
An area is a map boundary
Type 1 and Type 2 LSAs stay inside their area. An area border router participates in more than one area and keeps a separate LSDB for each attached area.
Meet Area 0
The backbone connects non-backbone areas in the normal OSPF hierarchy. Plan a contiguous Area 0 and attach other areas to it. A virtual link is a specialised tool with constraints, not a substitute for a sensible backbone.
ABR is not ASBR
An ABR connects areas. An ASBR introduces external routing information into OSPF, for example by redistribution. One physical router can perform both roles, but the roles answer different questions.
Stub and NSSA
A stub area blocks AS-external Type 5 LSAs and uses a default route for external destinations. An NSSA also excludes Type 5 LSAs but can originate external information locally as Type 7 LSAs. Eligible Type 7 information can be translated into Type 5 by an NSSA translator.
Avoid this shortcut
An ABR does not simply forward every LSA unchanged into another area. It originates information appropriate to the destination area. Follow the LSA types to see the difference.
Protocol reference: RFC 2328 (OSPFv2). NSSA reference: RFC 3101.