Are carpal tunnel syndrome and repetitive strain injury the same?

No!: Carpal tunnel syndrome is a constellation of symptoms (pain, numbness, weakness) associated with compression of the median nerve at the level of the wrist. Repetitive strain injury is an inclusive diagnosis to describe injury to musculoskeletal tissues due to repeated motions over extended periods of time (e.g., assembly line work or excessive gaming). Rsi can lead to cts, but most cts is not rsi.

Carpal tunnel RSI: Beyond genetic predisposition, carpal tunnel syndrome is related to overuse and misuse of the hand/wrist. Very often, this same misuse/overuse of the upper extremity can predispose to rsi conditions such as tendonitis of the wrist and elbow, not to mention worsening of neck problems.

No: 'RSI' is not a true diagnosis but a portmanteau term for any problem thought to be due to over-use of a limb. It covers a wide variety of real diagnoses with different treatments so whenever anyone tells you you have 'RSI' the first question you ask should be "OK but what is the diagnosis?"