Cognates revisited

Though my previous definitions for "cognate" and "false cognate" are what I generally have used, I have since discovered that I am not precisely correct. I'm not sure I fully like or agree with what the authorities say on the subject, but here it is (in my own words):

cognate. n. A word that shares root with another word.
false cognate. n. A word that appears to share root with another word, but does not.
false friend. n. A word which appears to share meaning with another word in another language.

I personally don't find these definitions nearly as useful. This means that "opened" and "unopened" are technically cognates, even though their meanings, while related, are exact opposites. And the term "false friend" for me seems very inappropriate in a technical or linguistic context. Surely there must be a better term, and if there isn't, why don't we make one?