Are non-Theravada monks allowed to eat after noon, and to use money? What's the history behind this? I am assuming non-Theravada monks eat after noon, and use money. Correct me if I'm wrong.

If I'm not wrong, why do the sects differ in this manner?
They differ for any number of reasons.  For one, there are at least five different 'official' versions of the vinaya - each of which is prominent in different countries.  The rules in each vary slightly - some have more rules, some have less, some place greater emphasis on different things, etc.  A lot of it also has to do with tradition and the culture where Buddhism is practiced.  If there is one thing you say about Buddhism it's that it very much malleable to local custom.  

A very good example of this is Japan.  Some monks there will accept money such as for funeral services.  Many will eat after noon, despite the injunction not to - it's just called "medicine" instead of a meal!  My own teacher's teacher really loved his sake despite that being a fairly clear violation of the fifth precept.  Some Japanese monks, believe or not, even get married.  

I think it's helpful not to view Buddhism as a monolithic entity.  It really is as complex as the people practicing it.