They are so similar that I had to turn to the dictionary to find a good explanation for how their meanings differ. :)
Merriam Webster explains the difference like this:
"pacify, appease, placate, mollify, propitiate, conciliate mean to ease the anger or disturbance of."
"pacify suggests a soothing or calming. ⟨pacified by a sincere apology⟩"
"placate suggests changing resentment or bitterness to goodwill. ⟨a move to placate local opposition⟩"
From here:
https://www.merriam-webster.com/dictionary/placate
Personally, I think of "pacify" as taking action to address a person or group's angry actions, while "placate" is taking action to address a person or group's angry feelings. (One deals with actions and the other feelings.) For example, you may pacify a crying baby by giving them a pacifier (to get them to stop crying) but you might placate a fussy baby by talking to it and amusing it until it's happy.