I've got a YouTube video on this.
Short answer: Use mock
when you're passing in the thing that you want mocked, and patch
if you're not. Of the two, mock is strongly preferred because it means you're writing code with proper dependency injection.
Silly example:
# Use a mock to test this.
my_custom_tweeter(twitter_api, sentence):
sentence.replace('cks','x') # We're cool and hip.
twitter_api.send(sentence)
# Use a patch to mock out twitter_api. You have to patch the Twitter() module/class
# and have it return a mock. Much uglier, but sometimes necessary.
my_badly_written_tweeter(sentence):
twitter_api = Twitter(user="XXX", password="YYY")
sentence.replace('cks','x')
twitter_api.send(sentence)