What is correct: "mobile" phone or "cell" phone? 

Same thing. The word cell is short for cellular and has been used since Bell Laboratories set up the first wireless telephony system in 1947. It consisted of a network of low-powered transmitters, each placed to cover a small region or cell. Commercial cell phones were introduced in Chicago in 1978 and in Europe in 1981. If you're surprised to learn that mobile telephony has been around so long, here's another surprise: Bell Laboratories invented the videophone in 1927.