El can be used for "any gods" but the word Shaddai means "All Mighty" or "The Almighty One" to differentiate him from all of the false gods.
As you may already know the first usage of this is in Genesis with Abram. It is right before the birth of Isaac, and in relationship to the new relationship that the L-RD now was to have with Abram. Abram is 99 years old and the L-rd makes his covenant with him and changes his name to Abraham, because he is to become a father of many.
The L-RD has appeared to Abram 6 times before this and this is the seventh time. The L-RD Himself tells Abram that He is "El Shaddai" , the Almighty G-d and to "walk before Him and be perfect". This lets Abram know that He is all -sufficient for all his needs and can accomplish all His promises to Abram.
This is the beginning of the fulfillment of the promise made in the garden. the L-RD is setting aside for Himself a special people to raise up His redemption from. It will not be through mans way ( Sarah gave Hagar to Abram so that he might have a son) but through the power of G-d Almighty alone ( the miracle child Isaac, from Sarah) that he will bring forth the promised child through.
This reavealing of Himself as the omnipotent, omnipresent, omniscient, and
All-Sufficient One is next found to the son of the promise, Isaac, in Genesis28 where Isaac sends Jacob for a wife and blesses him in the name of El Shaddai.
Then Jacob himself is "personally introduced" to El Shaddai himself in Genesis 35 when the L-rd changes Jacob's name to Israel and tells him of the land covanant that is to be passed to him and his seed forever.
Job refers many times to G-d and then in second reference The Almighty, or Shaddai, but not togehter. An example of this is in Job 33:4
The Spirit of G-d hath made me, and the breath of the Almighty hath given me life"
Many believe the book of Job is the oldest in the Bible and could have been written during the Patriaches time.
You may find some interest in this:
God is also known as El Shaddai. This Name is usually translated as "God Almighty," however, the derivation of the word "Shaddai" is not known. According to some views, it is derived from the root meaning "to heap benefits." According a
Midrash, it means, "The One who said 'dai'" ("dai" meaning enough or sufficient) and comes from the fact that when God created the universe, it expanded until He said "DAI!" (perhaps the first recorded theory of an expanding universe?). The name Shaddai is the one written on the
mezuzah scroll. Some note that Shaddai is an acronym of Shomer Daltot Yisrael, Guardian of the Doors of Israel.
The letter Shin is used on many mezuzah holders to stand for Shaddai. The letter shin can be read about in this forum under that title.