More exactly, Common was distinguished from customary law, which was different in each community; from the Law Merchant, which applied only to sellers of goods; from admiralty law, which applied to ships, sea-going matters, and salvage; from canon or church law, which covered wills in addition to internal church matters; and from Feudal law, which applied only to those holding land under Feudal tenure. Common law was also known as "the law of the land" the phrase usually used in translations of Magna Carta (The Great Charter).
Local courts continued to administer customary law, and Feudal to adminsiter Feudal law.
Later Common Law was distinguished from Equity, but still later equity and common law were largely merged.
Common law was "common" in the sense that it applied to all people in all places (in England, later in the UK), and that courts in one place would accept as precedent decisions from courts elsewhere.
The three major common-law courts were the Court of Common Pleas, the Court of the King's Bench, and the Exchequer court. Exchequer handled largely financial issues and tax issues (its name has the same root as cheque, and originally refereed to the checkered table used as a sort of early spreadsheet). King's Bench handled mostly criminal matters, but some non-criminal as well. Common Please handled a little of everything.
For lots of well-written history of the common law, from its earliest recorded period thru about 1970, see The Law of the Land by Charles Rembar.