The fact that the same coefficient captures both elasticity of substitution and risk aversion causes some problems in growth-style models with uncertainty (like capital asset pricing models and Ramsey-based RBC models). And just intuitively, there is no reason to think that a person who is say risk averse, MUST regard consumption in different periods in a particular way. Some of the newer behavioral economics has sought to disentangle the two. I can't remember any papers specifically off the top of my head, but I believe Thaler has some stuff on it.

BTW, even though you say you never met a student who could explain elasticity of substitution, you link to the wrong thing. That page is about substitution between capital and labor. Here we're talking about the substitution between consumption today and consumption tomorrow.