The "powered" microphones generally have a preamplifier or buffer in the microphone itself, allowing a higher level / lower impedance output to whatever then are connected to.
That tends to mean that the are more sensitive than unpowered "dynamic" microphones.
Having a preamp close to the microphone element also means that can be much more delicate and lighter as it does not need to work as a generator, just do something that can be detected electronically.
That's why true condenser microphones are so highly regarded - they have a large but very thin and light diaphragm which will "track" air movements far better than a thicker and heavier diaphragm.
This is a typical condenser mic capsule:
https://microphone-parts.glopal.com/en-GB/p-544619139/rk-87-microphone-capsule.html?utm_campaign=en_US&utm_medium=pr&utm_source=microphone-parts.com
The commonest "good" dynamic mic is a Shure SM58; that's the ball-ended one you see in just about any live show.
https://d1aeri3ty3izns.cloudfront.net/media/4/44415/1200/preview.jpg
This is the capsule for one; you can see its only the diameter of the top of the body:
https://522bb370f5443d4fe5b9-f62de27af599bb6703e11b472beadbcc.ssl.cf2.rackcdn.com/product/list_image/7557/prod_img_r59_m.jpg
The construction is almost identical to a small loudspeaker, but working in reverse; a coil attached to the diaphragm moves in a magnetic field, generating a voltage.
See the source link for a diagram.
Note that a lot of microphones aimed at enthusiasts and labelled as "studio condenser" are scams - some costing $15, some costing $200 - $300 or more.
They have electret condenser capsules, which cost peanuts by comparison to a true condenser type. They are the same as used in all general electronics and basic ones cost a few cents each in bulk.
There are some true condensers at sensible prices but you need to be careful..
Examples of good ones - the MXL V67g ($100), MXL 990 ($80) and MXL V87 ($220).
A cheap fake one, for comparison - the Neewer NW-700. As that's only $15 it not bad value, but only the same capsule as a "PC Microphone" that sells for about 0.99 on ebay..