Probably more a comment than an answer--for whatever reason my browser won't let me access the comments so I am posting here.
[First, I changed the tag to "soft-question". That is more appropriate tag than "contest-math" where new posts are expected to bring up a contest question. Hopefully this will stop the down-votes.]
This is actually a really interesting question IMO and it brings up a point that many people get confused about I think. I'm not sure if your question about "levels" really fits what is going on. Do not confuse puzzle-solving ability with general mathematical background! Just because a question does not involve as much math background to state or even to solve does NOT mean that the questions is any easier! With that said, Math Olympiad questions tend to assume the mathematical background that an advanced student may have by the end of high school, whereas the Putnam assumes a general mathematics background of a university undergraduate student majoring in mathematics.
HOWEVER, that does not mean that Math Olympiad questions are easier than Putnam Exam questions! Or that they are not challenging for a PhD student or university professor. The harder ones especially are hard for most anyone, and really do require a clever insight. In particular, there are certainly high school students who are able to figure out Math Olympiad questions at least as well as a university professor, even though the university professor knows plenty of math that the talented high school student has not seen yet.
I hope this helps...