The confusion is easy to understand. While both words have numerous meanings and can be used as more than one part of speech, they have similar meanings when used in directions. The difference is reflected in the part of speech. Passed is used as the verb in directions, while past is used as a preposition, usually after a verb.
- Passed is used to express the action in a sentence.
[Passing is the action in the sentence. Doughnut shop and gas station are the objects of the verb.]
- Past is a preposition indicating a spatial relationship - one thing beyond another in space/location.
[Driving is the action in the sentence. Past is used to indicate a spatial relationship - where Lucinda is driving. In this sentence, doughnut shop and gas station are objects of the preposition, not the verb.]
Note that the prepositional phrase follows the verb. When deciding whether to use passed or past, the writer must determine whether the word needed will express the action in the sentence or the location of the action.
In Brief: Use the verb passed to express the action in a sentence; use the preposition past to indicate the location or direction of the action.