Swam is the simple present tense of the word, swim which simply means to traverse or move through the water without reaching the bottom. It requires staying afloat or propelling through the water via natural means.
"After the titanic collapsed, survivors swam to the shore for safety."
Swum is known to be the past participle of the word, swim. It has the same meaning as its root but the tenses differs.
"I already swum today."