I'd argue that boiled water very specifically refers to the water left ofter after boiling water, not steam. Steam is no longer water, at least not in common parlance.

Boiled water does have the extra connotation that it is presumed to be mostly sterile, which, while not hard to derive from the fact it has been boiling, is not immediately clear. After all the past tense does not tell us how recently it was boiled.

For that reason I'd argue that if one of boiling water and boiled water should be in the dictionary, it should be boiled water. Of the two, it is the term that potentially carries extra information.