The first one is past tense, and the second one is present/future. When I came home today... - 오늘 집에 왔을 때... When I go home today... - 오늘 집에 올 때... Edit: Please correct me if I'm wrong or give feedback if I didn't provide good enough answer. Don't just down vote.

-ㄹ때 and -ㅆ을 때 is an example of the verb ending -ㄹ, which has these two major applications. 1. creates an adjectival phrase with a noun that is tenseless. The tense is determined by the main verb elsewhere. It facilitates a verb-noun combination conveniently, usually with nouns like 때, 경우, 터, etc. for a time or occasion expression, freed from the tense specification. 2. creates an adjectival phrase indicating conjecture, expectation, possibility, requirement, etc. This usage often corresponds to the to-infinitive or subjunctive expressions in English, and usually goes with people or things. The past form -ㅆ을 expresses the resulting state or an earlier occurrence of an action, as opposed to the progressing action of the -ㄹ form. (#1 sense examples) - 엣날에 공무원일 떄가 좋았어. (past) Times were good when I was a civil servant long ago. - 엣날에 공무원이었을 떄가 좋았어. (the same, with a slight emphasis on having been in that post) - 옛날에 공무원이었던 때가 좋았어. (using -었던 instead of -ㄹ/-ㅆ을. It works but not as naturally) - 어릴 때의 기억 = 어렸을 때의 기억. (past) Both are widely used with little difference. 어린 때 and 어렸던 때 are strange. - 나갈 때 말하고 가. Tell me when you are going out. (future) - 지갑을 잃어버릴 때는 어떻게 하죠? (contingency) What do you do when you LOSE your wallet? (엃어버릴 is unnatural) - 지갑을 잃어버렸을 때는 어떻게 하죠? What do you do when you HAVE LOST your wallet? (more natural as it states the unexpected situation of having lost it) (#2 sense examples - usually don't involve time-related word like 때) - 내가 할 일 = things for me to do. - 내가 했을 일 = things I would have done (if some condition had been met) - this is more rare but possible. - 내가 결혼할 사람 = the person I will marry [for me to marry]. - 그 사건만 없었다면 내가 결혼했을 사람 = the person I would have married but for that incident. - 집에서 기다릴 아내를 생각하면 마음이 바빠졌다. I felt my mind rushing when I though how my wife would be waiting. - 집에서 기다렸을 아내를 생각하니 너무 미안했다. I felt so sorry thinking how my wife must have been waiting. (looking back on the earlier situation, so 기다렸을)