They are no different in the sense that most of the times they are used switches.
They are quite different in terms of what they can switch and how their switching behaviors are controlled.
- Mosfets, by themselves, can only switch DC current. Triac can switch DC and AC current.
- Mosfet is a voltage-driven device and Triac is a current driven device.
- Triac is self-sustaining and Mosfet is (practically) not self-sustaining. Once you have turned on a triac (it starts to conduct), it will remain conducting all by itself until the current reverses. Mosfets, because of its leakage, will turn off over time.
Mosfets can switch at much higher frequencies than a triac can. Triac can switch much higher current than mosfets can - being inherently a transistor, triacs' voltage drop is independent of current it swiches. Mosfet's voltage drop is linear to the current it switches, making the mosfet unsuitable for high current switching applications.