Is there an easy way to differentiate these from each other? I never know when to use which. Please help if you know.
"Passed" is the past tense of the verb "to pass." E.g., "She passed by the haunted house every day on her way to school." Or, "The car ahead of me was going too slow, so I passed him." Or, "I passed him the salt ten times in one meal." "Past" is a noun or an adjective referring to a time that is no more.* "The house used to be the social center of the community, but that was all in the past." Or, "The past president of our club was honored at a dinner last night." Or, "She is a past master at snooker." A good way to judge which one is correct would be to plug the word "pass" or "passes" into your sentence and see if it still makes sense. If it does, you need a verb: Use "passed." If not, "past" is what you need. *It's also, of course, a way of describing verb forms dealing with action that is completed. As in my first paragraph.
"In the past, I passed up on many chances to travel, but I'm past all that. I've gone past the one million mile mark in my frequent flyer club!" Which I suppose means that "past" can also be an adverb (yes?) referring to motion (figurative or literal) relative to something else. And darned if I can say that properly without using the word itself. EDIT: I'll try this: " . . . referring to the transit of an entity or body relative to another entity or body that is stationary or else moving at a slower speed than the subject entity or body." Clear as mud, right? Oh well.
It's being used as a preposition there, which can be functionally either an adjective or adverb phrase. This one's an adjectival preposition. You can make it easy by swapping an adjective for the phrase. That reveals its function. I am happy. (happy is a simple adj) I am past all that. (past all that describes "I" in the same way) But you're right. Past can be a preposition heading a phrase that's doing the job of an adverb. We ran outside. (outside is an adverb describing where the running was done) We ran past the graveyard. (the "where" of past the graveyard is also adverbial)