この間 means "the other day," and 最近 means "lately, " ”recently," or "these days."
例)
この間
ねぇ!あの子の靴(見て)!この間私が話してたものだわ!
Hey! Look at her shoes! They're the ones that I was telling you about the other day!
最近
最近カナとコウタはいつも一緒にいるね。あの2人付き合ってるのかな?
Lately Kana is with Kouta all the time. Do you think they're seeing each other?
hope it helps! :]