Control+T is the shortcut in Photoshop for Free Transform, which turns your selected region into a click+drag target for translating; the corners and edges become resize handles for the selected content; outside of the corners becomes a rotate click target. There's also now a context menu for more advanced transformations like Skew, Perspective, etc.
It's pretty much an all-in-one toolbox of most anything you'd want to do with a selection, and I could never find a good equivalent of that in GIMP.
Regarding the handles in GIMP - last I tried them, they resized the selection region, rather than the underlying image, which was immensely frustrating.
Ah yeah, that's nothing like what I thought you meant. That said, if I wanted to do something like that in Gimp, I'd just cut-paste - this creates a temporary layer with the content positioned exactly where it was before, where you can use the standard layer manipulation tools to transform it. You can then use either the "new layer" button to promote it fully, or "anchor" to paste it back onto the original.
I don't know what ctrl+T is (there may be some nuance I'm missing), but in Gimp the corner resize handles are always visible in a selection, the side handles appear on mouseover, and moving a selection is click+drag in the center.