Well, it's pretty obvious, that a variable that's never changed should be either const or read-only. The question which one of these is better depends on the situation. Const variables are by definition constant - their values should NEVER change (e.g. const int minutesInAnHour = 60;
looks like a good candidate). That's why the constant is a static member implicitly and it is initialized during compile time, i.e. the compiler might actually replace all the appearances of your constant with the literal value, though I'm not sure if any compiler actually does that.
Readonly, on the other hand, is a member variable whose value should not change, once initialized, meaning that it is not actually a constant, you can do something in the lines of readonly DateTime time = DateTime.Now;
. This, of course, will not be a static member, in fact it will be a normal member just with the restriction that it can't be changed once assigned. The benefit of this vs. const is that if your const variable changes in some build, other dependad libraries may not know that - they can even have the constant value comppiled in - you'll have to rebuild everything.
And as for the question why resharper suggests readonly vs. const - I'm not sure, I'd guess that a readonly variable is less restrictive and it figures that that's what the developer probably wanted.