1- My friend stopped to talk to me on his way home. --> meaning my friend stopped (doing something else such as walking in order) to talk to me (i.e. My friend was talking to me.)
2- My friend stopped talking to me on his way home. --> My friend shut his mouth and didn't talk to me (i.e. My friend was not talking to me.)
Yep, as Taiman said. The meaning of the two is quite opposite to each other: in the former your friend is about to start talking, in the latter your friend finished talking.
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