OWL is a family of languages for ontologies based on description logic. There are many (many, many) variants of OWL with subtly different syntax and semantics.
OWL 2 has two distinct semantics, the Direct Semantics and the RDF-Based Semantics. The Direct Semantics is compatible with SROIQ description logic, which is very well-researched, but places some constraints on ontology structure. Ontologies compliant with these constraints are informally called "OWL 2 DL" ontologies, and "OWL 2 DL" is used informally to refer to OWL 2 DL ontologies interpreted using the Direct Semantics.
The RDF-Based Semantics is compatible with RDF semantics and can be applied to any OWL 2 ontology. "OWL 2 Full" is used informally to refer to RDF graphs considered as OWL 2 ontologies and interpreted using RDF-Based Semantics.
OWL 2 has three different "profiles" (syntactic subsets) trading expressiveness for tractability. Each is more restrictive than OWL DL (so semantics are subsets of Direct Semantics). They are not strictly ordered with respect to expressiveness - they all just make different choices.
OWL 2 EL enables efficient execution of all the standard reasoning tasks (which?). Useful for very large ontologies.
OWL 2 QL enables efficient conjunctive queries using standard relational databases. Useful for simple ontologies over large data sets.
OWL 2 RL allows rules stated as descriptive logic programming rules, enabling efficient reasoning over RDF triples using rule-extended database technology. Useful for simple ontologies over large data sets where operating directly on RDF triples is desirable. Unfortunately, DLP rules are not very expressive.
OWL 1 has three sublanguages. In order of decreasing expressiveness (increasing tractability): OWL Full, OWL DL, OWL Lite. OWL Full is undecidable. OWL DL is designed to retain as much expressiveness as possible while remaining decidable. OWL Lite is not actually that much more tractable than OWL DL and isn't used much.
OWL 2 is backwards compatible with OWL 1.
OWL is a W3C project, built on top of RDF. It sort of supersedes RDFS, which was a language for shared RDF vocabularies, but apparently had some shortcomings (??)
OWL 1 was originally based on DAML+OIL.