QA in Agile and Waterfall, is there a difference?

Let's try altogether to create not even exhaustive and full, but acceptable for all of us classification \ topology of testing types, starting with "wide brush moves" "static" and "dynamic" and finishing with complicated terminological names of exact types. I'll be honest with you - I couldn't find really good classification from the box... even if we speak about world famous certification like ISTQB... That why our work made beforehand is valuable itself... it's important for all from junior specialists to Pre-Sales Technical QA Consultants... this topology is a base for professional coordinate axes of any testing specialist... But we are going deeper: through the cooperatively formulated QA topology we're going to look at software development methodologies not in abstract terms, but in real life, will learn common and different things in Agile and Waterfall methodologies in the QA context. I hope the report is going to be useful not only for QA specialists and PM's but ...