Since this question is about international relations, I would add that they also had different opinions on how to combat fascism. Stalin favoured a popular front approach which would include allying with liberal democrats and anyone else opposed to fascism whereas Trotsky, viewing this is class collaborationist, argued for a stricter coalition called the United Front which would include Social Democrats but not bourgeois parties.

This followed Stalin's previous "third period" position that capitalism was about to collapse and that communists should therefore treat Social Democrats with hostility as they were nothing more than "social fascists." This mistake was especially bad in Germany where Hitler benefited from division on the left in his rise to power, (although the Social Democrats were also hostile towards the Communists.)

edit:

It would appear that the first answer in this thread has been removed, probably because the author blatantly inserted their own bias at the end. to summarize: their differences when it comes to international relations where is that Trotsky was insistent on trying to spread communist revolutions across the world, a position that was called permanent revolution. Stalin on the other hand, while not opposed to seeing other countries go communist for obvious reasons, instead focused on maintaining socialism in the Soviet Union. This position was called socialism in one country. It often contradicted Trotsky's goal of permanent revolution because the capitalist countries, especially wealthy ones, were hostile towards the Soviet Union even before the era known as the Cold War. It was seen as safer to peacefully coexist with these regimes rather than call for their overthrow.