If I mention my work, is it correct to say "tasks" or "assignments"?
In your work, Ruby, it is correct to use both. Let me give an example;
I work as a web designer, and each client has an assignment for me, for example a project to design their home page, and I divide the assignment into tasks, such as designing the header, menu, content area, and footer. My price can be for the assignment, or the client can pay for individual tasks.