In this case, ("When I saw") I think both are the same.
But as Emir said, if you change the pronoun "I" to something else like "you", according to the pronoun you should change "gördüğümde". But no need to change "görünce".
When I saw----> Ben gördüğümde
When you saw----> Sen gördüğünde
When I saw--->Ben görünce
When you saw---> Sen görünce