This is a short expository paper discussing the different notions of equivalence, such as simple equivalence, contact equivalence, and divergence equivalence for variational problems with one independent variable. I show that the group of symmetries under one notion of equivalence can be distinct from the group of symmetries under another notion. I discuss how one can set up the equivalence problem to compute these different groups of symmetries, but do not enter into any actual equivalence calculations.
Please note: This paper was typeset directly from my handwritten manuscript (nearly the last handwritten one I ever produced) and I did not get to proofread the result before it appeared. Consequently, there are many typos, particularly in the matrices on the last pages.