To simplify it, we could say that:
- A Thunderbolt port is also a mini DisplayPort.
- A mini DisplayPort is not necessarily a Thunderbolt port.
If you know your Mac has a Thunderbolt port, you can use any cable/accessory that is for mini DisplayPort.
If you have a mini DisplayPort that you know isn't a Thunderbolt port, you can use mini DisplayPort cables/accessories but not Thunderbolt cables/accessories.
To answer your question, your Mac has a Thunderbolt port which means you can use a mini DisplayPort accessory like a mini DisplayPort to HDMI adapter. There aren't HDMI adapters that works only with Thunderbolt ports but not regular mini DisplayPort, that's why they don't call them Thunderbolt to HDMI adapters.
Mini DisplayPort is designed for audio and video signal, but not data. Stuff that use data transfer like external drives, hubs, FireWire/Ethernet adapters and such are all Thunderbolt-only and won't work with a regular (non-Thunderbolt) mini DisplayPort.
