I found both 大州 and 大陸 in this sentence, I looked them up on Jisho and I see they both mean "continent". Is there any difference between them? Are they interchangeable?
六大州 is the name for "The Six Continents". The difference between 大州 and 大陸 is maybe best illustrated by an example:
大州: （例） ヨーロッパ州 = 欧州 = Europe
大陸: （例） ヨーロッパ大陸 = Continental Europe = mainland Europe
Strictly speaking (according to Wikipedia), the difference is that the 大州 includes surrounding islands, whereas 大陸 refers to the main landmass of a continent.
This is consistent with the fact that the continents themselves are referred to as 〇〇州 and their mainlands can be referred to as 〇〇大陸.
The sentence would appear to be more correct if it said
However, even monolingual dictionaries such as 大辞泉 or 大辞林 don't note this difference, so it appears that 大州 is not really used as an individual word and 大陸 is used for "continent" in both senses. (The same is true in English, I think.)
The two words are conceptually very different (I'm surprised they share the same word in English, honestly).
If you find the above not enough clear, try think about Oceania. Oceania (オセアニア) is a 大州, but not a 大陸, because it mostly consists of reefs and volcanic islands. What is 大陸 is only Australia.
You could refer to dictionaries for how we count five "continents" of each: