First of all, it makes no difference really to us users. A good mic is a good mic regardless of whats inside it. For all I care it could be chicken manure as long as it sounds good. There is a tradition here, but it is more about tradition than about real differences. Good microphones could conceivable be made using a lot of different techniques, evolving over time -- just witness how hip ribbon mics has become lately, earlier a more or less dead technology.
All types in the question are condensor mics, also called capacitor mics as they work on the capacitance changing in the condensor mic element. In order for them to work you need a polarizing voltage in the mic. It can be supplied from the outside (battery or phantom) or it can be permanently "burned" inside the mic.
Electret condensors has the polarizing voltage burned into a plastic membrane. This was a rather recent innovation (60-s or so). The first versions had the polarizing voltage burned into the front membrane, a technique still used at times.
Later versions moved the polarized membrane to the back, allowing the front membrane to be made thinner or even from other materials. There are some really good back electret mics around. One example is that most, if not all, of the DPA mics (former B&K) use that technology. My DPA 4003-s, generally acclaimed as among the very top omni mics, are internally back electrets with a stainless steel mic membrane.
(Extra: For the really interested only true pressure omni mics can be made with the very stiff stainless steel membrane. Cardoids require much softer membranes).
Most condensor studio mics today are made in China (if you count them) and most use externally polarized condensor capsules. This generally means that they need phantom power. Some are good, some not.
All condensor mics, regardless of type requires some kind of electronics inside them, often called a head amp. The reason is that the signal from the mic element can not travel very far before detoriating. We are probably talking a few inches as maximum here. So there is at least one transistor or tube inside the mic casing. This head amp needs some kind of power supply which could be as little as a 1,5V battery, phantom power or even a special 200V external power supply.l
So to summarize: It makes a difference to the producer what technology to use. To the user all that counts is the result.
Gunnar