From what I understand, a Syder is usually a car that has a "soft" top that you can pull up or down, and that it's meant to keep the general shape of the car regardless of whether it's up or down. And a roadster is a car that is either meant to never have a roof, or has a removable "hard" top.
Convertible is any car that allows you to choose to have the top on or not (like you can remove it or fold it or put it back on).
Targa is when it has a piece of the roof can be removed.
I could be wrong though, I never paid much attention to how specific the terms were :Phttp://www.lamborghinipalmbeach.com/blog/whats-the-difference-between-a-spyder-and-a-roadster/https://en.wikipedia.org/wiki/Targa_top