You can connect each AP to the controller directly, because you only have two APs and you happen to have two distribution ports on the controller. If you wanted to connect more than two APs to your WLC4402 you would need a switch.
The ports that "are not ethernet" actually are ethernet, but you can't plug any cable directly into them. They're called SFP ports, and you must insert a transceiver into the port before it's usable. In your case you probably want to purchase a couple GLC-T copper transceivers so you can use CAT5/6 with a regular RJ-45 connector, although fiber transceivers are also supported by the controller. You could also buy only one SFP transciever and use it to connect the controller to an old switch if you happen to have one. From there you can connect <= 48 APs.
Have you read the quick start guide for the WLC? It has a lot of good info!