Are they generated by different phases of a compiling process? Or are they just different names for the same thing?
From what I understand, the AST focuses more on the abstract relationships between the components of source code, while the parse tree focuses on the actual implementation of the grammar utilized by the language, including the nitpicky details. They are definitely not the same, since another term for "parse tree" is "concrete syntax tree".
I found this page which attempts to resolve this exact question.