Difference betwee storage class and type (invariant/const)?

[Robert Fraser]

Can someone explain to me what the difference is between a storage class and a type is, with regards to const and invariant? For example, what do these do differently?

invariant int foo;
invariant(int) foo;

...? I know this is probably second-nature to people with C++ backgrounds, but I find the documentation quite confusing, as I've only really worked in Java before.