These words have separate origins, but today the meanings differ only slightly. In my mind, "stand" and "tolerate" are quite close, implying inconveniences less than severe. On the other hand, "endure" and "bear" suggest more difficult hardships. "Bear", for example, also has the meaning "to give birth". I should add that "endure" and "tolerate" have Latin or Greek origins, so those two words are more academic.