The word comes from England, the country that famously doesn't play modern baseball.
The earliest reference to baseball comes in a diary entry of a Surrey solicitor, William Bray. On Easter Monday, March 31st, 1755 Mr Bray refers to playing 'base-ball' with his friends.
Went to Stoke church this morn. After dinner, went to Miss Jeale’s to play at base-ball with her, the 3 Miss Whiteheads, Miss Billinghurst, Miss Molly Flutter, Mr. Chandler, Mr. Ford, and H. Parsons. Drank tea and stayed till 8.
Are baseball, rounders and softball the same?
No. They share features but have different rules, traditions and histories - see here.
As Scyld Berry points out, the claim that America's summer sport descends from the English game of rounders does not 'get to first base'.
More on the relationship between the rival summer games of 'two countries divided by a single language' here.
What is 'inside baseball'? * What is a curved ball?
More on the relationship between the rival summer games of 'two countries divided by a single language' here.
What is 'inside baseball'? * What is a curved ball?