Well, I've never worked with Keyence before, but I can speak generally.
A relay output sends current to a relay inside the output card, which pulls in a coil, which allows current coming in from the field to flow through a contact. So you need to provide an incoming current wire as well as an outgoing current wire which leads to your field device (light, solenoid valve, etc.) for each output.
With a transistor output, when the PLC turns the output on, it sends a voltage to switch the transistor "on", which allows current to flow through the transistor. Usually, (at least with the A-B stuff I've used) there is one incoming current line to the whole card, which goes to each transistor. Then, when a transistor is turned on, the current flows to the outgoing terminal and to the field device. So with the transistor output card, you have one wire per output, instead of two per output on the relay card.
One advantage of the relay card is in most cases you can have AC and DC outputs on the same card.
I wish I had time to put some pictures together to make this clearer, but I've got to run to a meeting now. Hope this helps!