Yes, unfortunately, it does matter. Each of your "coils" actually consists of two coils of wire. One is the primary and the other is the secondary coil of a transformer. All four wires need to connect to something for the circuit to work. It just happens that one wire from the primary and one wire from the secondary connect to ground. The other primary wire goes to the points, and the other secondary wire is the spark plug wire. If you are lucky, you have anough of that solid wire protruding that you can somehow connect to it. Perhaps by soldering another wire to it.
Thanks for the info. The old coils had become soft and had cracks in them. I will try to connect the wires together if possible. I will let you know how the processes turns out.
Thanks again for the help.