Jaffles and their associated machine are represented here

Toasties here and here, and here, and here where it doesn't even have a lid, and this one which should really just be called a Reuben but the Aussies stick "toastie" on as a suffix.

Note the variety of breads and fillings. Toasties are a very flexible concept.Those toasties have been cooked any number of ways, under a grill (broiler to the yanks), in a pan, hell even a toaster followed by a microwave, also very commonly in one of these, a sandwich press, which as you can see is flat and and does not seal. Those also sometimes come with little ridges for grill lines like the American panini presses, but I prefer this style as it's more versatile.

If you google image search toasties you'll probably see a few jaffles in the results but if you search jaffles you're going to pretty much only see... jaffles, which have that characteristic shape imposed by that particular machine.

In conclusion all jaffles are toasties, but not all toasties are jaffles. If it's been made in a machine that imposes that particular jaffle shape on to it by way of sealing the sandwich in like a waffle iron, then it's a jaffle.