The Celts are people who made up the various tribes. They were called Galli by the Romans and Galatai or Keltoi by the Greeks, terms meaning barbarian. It is from the greek Keltoi that Celt is derived. Since no soft c exists in greek, Celt and Celtic is pronounced with a hard K sound.
When the British Empire was distinguishing itself as better and separate from the rest of humanity, it was decided that British Latin should have different pronunciation from other spoken Latin. Therefore, one of these distinguishing differences was to make many of the previously hard k sounds move to a soft s sound, hence the Glasgow and Boston Celtics. It is the view of many today that this soft s pronunciation should be reserved for sports teams since there is obviously nothing to link them with the original noble savegery and furor associated with the Celts.
Scotland got its name from the Scots who first arrived in Argyll in the latter part of 3rd century. The Scots were a people who spoke Irish, not Scots. The Scots language is not Celtic, it's a German dialect heavily influenced by Gaelic.
. . . and as for Scotch? . . . Well, scotch is an alcololic beverage and should never be used when referring to people, it's considered a wee bit offensive. It's a term used to mean various things, but not people. Generally you would use Scots for people and Scottish for everything else.
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