Bloc means a group of nations or people united by common interest. This is its primary definition, but it is occasionally used in a variety of other senses that make it roughly synonymous with group or alliance. The much broader block has a variety of definitions, but a group working together is not one of them.
Though the words are different in modern English, they share a common origin in the French bloc. Block came to English many centuries earlier, however, first appearing around the 13th century. Bloc in its modern sense didn’t arrive in English until around the beginning of the 20th century.
Block is often used in place of bloc. For example, these writers seem to mix them up:
Blatter will receive a fourth term in office amid rumors of the 46-member Asian voting block walking out of the meeting. [Star-Ledger]
Adopted back in 1974, this amendment introduced sanctions against the Soviet Union and other countries of the Communist block. [The Voice of Russia]
Palestine and Israel – along with Jordan, Egypt, Turkey Syria and Lebanon, are the basis for a new economic block that could grow as time moves on into the 21st century. [Milford Daily News]
And these writers spell bloc correctly:
British shareholders make up an important voting bloc on the companyboard. [Guardian]
NATO members in the ex-communist bloc are wary of moves to bring Russia on board in an anti-missile system. [The Australian]
Europe’s economic bloc has played an important role in driving global copper consumption. [Wall Street Journal]