Why is "!=" used with iterators instead of "<"?

I'm used to writing loops like this:

for (std::size_t index = 0; index < foo.size(); index++)
{
    // Do stuff with foo[index].
}

But when I see iterator loops in others' code, they look like this:

for (Foo::Iterator iterator = foo.begin(); iterator != foo.end(); iterator++)
{
    // Do stuff with *Iterator.
}

I find the iterator != foo.end() to be offputting. It can also be dangerous if iterator is incremented by more than one.

It seems more "correct" to use iterator < foo.end(), but I never see that in real code. Why not?