The Short Answer
The three standards are successive steps in how much power Ethernet can carry. 802.3af delivers about 15 W per port, 802.3at (PoE+) about 30 W, and 802.3bt (PoE++) up to 60 W (Type 3) or 90 W (Type 4). af and at use two of the four cable pairs for power; bt uses all four.
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802.3af (PoE) ~15 W at the source, ~12.95 W at the device: cameras, VoIP phones, access points.
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802.3at (PoE+) ~30 W: PTZ cameras, video phones, larger access points.
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802.3bt Type 3 ~60 W: video conferencing, multi-radio access points.
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802.3bt Type 4 ~90 W: PoE displays and panel PCs.
Which You Need
Match the standard to the most demanding device on the link, and remember the power available at the device is a little below the source figure because of cable loss. A PoE+ or PoE++ source covers most edge deployments.
See our guide to industrial Power over Ethernet for the full picture.