I think both mean "Even so" or "nevertheless"
The difference is rather huge even though the two words do overlap in meaning to an extent. When a bilingual dictionary gives you the same English "definitions" to two Japanese words, the best thing to do is go to a monolingual dictionary.
「それでも」 is a contradictory conjunction.
「雨{あめ}も風{かぜ}も強{つよ}かった。それでもピクニックに行{い}った。」= "It was really rainy and windy. We, however, still went on the picnic. "
「毎日{まいにち}１２時間勉強{じかんべんきょう}したが、それでもテストに受{う}からなかった。」 = "I studied 12 hours a day, but I still did not pass the test."
「ところが」 is used to talk about an unexpected result.
「その映画{えいが}の評判{ひょうばん}は良{よ}くなかった。ところが実際{じっさい}に観{み}に行{い}ったらとてもよかった。」 = "That film had bad reviews. Even so, I loved it when I actually went see it."
「8回{かい}まで5対{たい}0で勝{か}っていた。ところが9回に6点取{てんと}られ、負{ま}けてしまった。」 = "We were leading 5-to-0 at the end of the 8th inning, however, we gave up 6 runs in the 9th inning and lost the game."
