"I found you."
What is the difference between Znalazłam cię and Znalazłem cię? Is this simply a case of either spelling being correct? (Like Advisor/Adviser in english)
No. it is a difference in gender. A man will say "znalazłem", a woman "znalazłam".
This is a rule for all past forms - a for feminine, -e for masculine , -o for neuter (only in third person-it)
also -i for "oni" groups (at least one man), and -y for "one" groups, (everything but male people)