First of all, the AIFF stands for Audio Interface File Format, while the full meaning of AAC is Advanced Audio Coding. The two are coding algorithms that are mostly used by Apple products. These two codecs show how the audio is recorded and digitized in digital format. The way by which encoding is done in both AIFF and AAC makes a significant difference between them.
AIFF is known to be a lossless format, which simply indicates that nothing is lost in the audio information, but they are all kept in the file. The quality of sound remains the same irrespective of the number of times you encode the file.
AAC, on the other hand, makes use of a lossy compression algorithm, which discards information that is considered less important. When you convert a lossy to a lossy or a lossy to a lossless codec, the more you do it, the more it gets worse in quality.