Both さけ and しゃけ mean salmon and are written as 鮭 in kanji (but I will avoid using this kanji in this answer for an obvious reason). As far as I know, there is no difference in meaning, but some people seem to distinguish the two words in meanings (see below).
According to a webpage by Maruha Nichiro Foods, Inc., the Kōjien dictionary lists the word しゃけ as a variation of the word さけ with the same meaning. The webpage also states that there is no obvious geographical tendency between the use of さけ and しゃけ.
According to this page and this page, some people distinguish the two words, in which case さけ means living or raw salmon and しゃけ means cooked salmon. I had never heard of this distinction personally, and I doubt that many people distinguish the use of the two words.