Regarding the arcane lingo: In After Effects 7 and CS3, the terminology changed with the introduction of the new user interface. The Composition window was replaced by the Composition panel, the Layer window by the Layer panel, et cetera.
For more information about the terminology for user interface items in After Effects (and other Adobe applications), see the “About workspaces” section of After Effects Help.
Regarding opening text layers in their own layer panels: As Dave says, you can’t open text layers (or shape layers, or other layer types not based on footage items in the Project panel) in their own Layer panels.