"I found you."

Translation: Znalazłam cię.

[derpderp11]

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)

[immery]

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)