Rigorous refers to something that is strict, thorough, or exacting. It is often used to describe a system or process that requires a lot of effort or discipline. For example, "The university has a rigorous admissions process."
Vigorous refers to something that is strong, powerful, or forceful. It is often used to describe an action or movement that is characterized by high energy or effort. For example, "The athletes performed vigorous exercises to prepare for the competition."
So, while both words refer to something that is demanding or challenging, the emphasis slightly differs. Rigorous emphasizes the strict or exacting nature of something, while vigorous emphasizes the energy and force of something.