Is tendonitis of the wrist similar to a sprained wrist?

Not really. Tendonitis is inflammation of a tendon sheath (the tight passageway where tendons glide). A sprained wrist is an injury of the ligaments of the wrist. Tendons move joints and are attached to muscles. Ligaments connect bones to other bones across joints. Both can happen after trauma (a fall or twisting injury), but a sprain doesn't happen over time like tendonitis can develop.
Similar yes. Not exactly tendonitis is inflammed overused tendons a sprain is injured strteched ligaments from a fall or trauma.

Related Questions

I caught a heavy binder & it bent my wrist backwards. The cyst arose from that trauma. Diagnosis was sprained wrist & tendonitis but it's been 10 mos.?

Wrist Pain. May represent a wrist ligament injury, ganglion cyst, or tendon insertion injury by your description. If not improved after 10 months i would have evaluated by musculoskeletal or hand specialist. Read more...
X-rays can help rule. Out a more severe injury or a ligament injry that needs attention. If a cyst formed it may not just go away by itself as well. If xray is negative and a ligament injury or fracture is still suspected then at times more advanced imaging is used such as mri. Read more...