In the House of Representatives, “an amendment must address the same subject as the matter being amended.” The word for this is germane. “The germaneness rule was adopted by the House in 1789 and has remained the same since it was last changed in 1822.”
The House Rules Committee calls it “one of the key procedural differences between the House and Senate.” In the Senate, on most bills, “amendments may be offered which have no relevance to the subject matter of the bill.”