The difference between ‘passed’ and ‘past’

The word 'passed' is the past simple of the verb pass or the past participle of the verb:
Example 01: She passed the exam with distinction. Pass = to be successful in a
Example 02:The secretary passed the message to me. Pass = hand over (give)
Example 03:We had passed the shop 5 times before we saw it. Pass = to move past

The word 'past' is not a verb. It has several uses. 'Past' is usually related to a time before the present or to indicate movement - from one side of a point to another.
Example 01: This past month was a difficult time for me.
Example 02: Thankfully all the trouble we had with the neighbors is all in the past.
Example 03: John ran past. He didn't even see us.