The harnesses will be different. You should get a wiring harness adapter for your specific car from the same place that sells the adapter plate to make the stereo fit the dashboard. You connect the wires from the Sony harness to the corresponding color wire on the adapter, and then the adapter plugs right into the car's harness. Never cut the wires inside the dashboard!
I usually solder and use heat-shrink tubing, because it takes me just a few minutes, and it makes the strongest, neatest connection. You can also use solderless connectors. If you must do the old twist-n-tape, make sure you tape each wire up neatly and tightly, and use a good electrical tape, such as 3M brand Tartan. I do this work at a table or a workbench, where there is plenty of room, prior to tackling the work inside the car.
Sound Domain is a nice, inexpensive place to order these parts from. Lately, brick and mortar stores all tend to gouge a significant margin out of these essentials, like they do with $30 USB cables. :|