The wired versions are the CM-311A and CM-312A. The wireless versions are the CM-311AE and CM-312AE.
The headband and mic elements are the same on the wired or wireless versions. The wired versions can be used with phantom power or powered by an internal 9V battery. If you want to use your mic "wireless" sometimes, and "wired" other times, that is best achieved with the CM-311A or CM-312A models. The important thing to consider is that you will be wearing the mic electronics AdaptaPack AND your transmitter, and using batteries in both, but this setup will give you added flexibility.
The wireless head-worn versions (CM-311AE and CM-312AE) can ONLY be used with a compatible "three-wire" wireless transmitter of your choice (see the FAQ concerning wireless systems above). Adding an XLR connector to those models and plugging them into your sound system directly will result in damage to the microphones.