Okay, so I'm to understand subspace is an action which takes place in a lower dimension and hyperspace a higher dimension.
In that sense, in sub-space, because there's less of it, you can transverse it much faster than conventional space -- though its constants are unfriendly to organic life that isn't spatially shielded some how - making it ideal for transmission.
On the other hand, hyper-space is harder to transverse but can be used to fold the lower dimensions through eachother - like an ant walking from one end of a newspaper and appearing on the other because the newspaper has been rolled over, with its ends meeting.
Just want to make sure my definition matches your definition, folks.