Would someone please explain how the Japanese would most naturally state that two "words" (関係 and 関連 for example) have approximately the same meaning?
My best bet is either
「関係」と「関連」の意味は同じぐらいです。
or
「関係」の意味は「関連」のと同じぐらいです。
Do either of these sound more natural? And for that matter, are they both grammatical?
The most natural way is probably:
「関係」と「関連」は同じような意味（の言葉）です。
「関係」と「関連」は似たような意味（の言葉）です。
You can also swap particles to say 「関係」は「関連」と…, in this case, the subject will be different but the meaning is practically the same.
(In case you might wonder why we can end the sentence with 意味です even though they are "words" and not "meanings", it's a kind of difficult matter to explain, but you can think in a way that [noun]だ sometimes stands for "be of [noun]" instead of "be [noun]".)
ぐらい is only used for comparison of amount (high or low, big or small etc.), and in this context you can't compare "how much meaning" they have.
