As Jura had said, the meaning is the same. However, there is a very subtle difference in the two sentences. "That night" emphasizes a particular night where as "in the night" just tells us that during one night. On the same note, there is also a subtle difference between "In the night" vs "at night". When you have such questions, it is best to Google for the explaning by typing, "difference between XXX and YYY".

Both mean the same

both are correct however "that night" sounds more natural