Is there any deeper meaning in the fact that the word "statement" starts with the word "state", or is that just a curious coincidence? Note that english is not my native language, so the answer might be obvious to you, but not me ;)
The English word "statement" does derive from the verb form of "state", but the programming terms "state" and "statement" aren't related to each other in any meaningful way. A statement in a programming language is merely a syntactic construct and does not imply that any state is involved.
Etymologically, the answer is yes, as Christopher pointed out.
However, I would argue that in programming, too, there is a connection. Statements (as opposed to expressions, which are syntactic elements which may be evaluated for their value) are syntactic elements representing imperative commands. (You may hear that in C, many statements (ex. assignment) are also expressions.)
As such, statements necessarily involve some change in the state of the program (ex x := 5
), or the imposition of some control flow (ex GOTO 10
).
You will note that a purely functional language (say, Haskell), contains no statements, but only expressions.
The key concept of imperative programming paradigm is that programs are represented by the sequence of statements one of which change the program state.
So you change the state or you can say you actually state (declare) something with each statement. For me it seems that -ment suffix is used here in its third sense ("The means or instrument of an action"). Statements are instruments to state something in imperative program.
In universal usage it seems that -ment suffix is used in its first sense ("An action, process, or skill").