The name El in the Bible
El is the generally accepted shortened form of Elohim, the genus God. Etymologically, however, the link may not be so strong. In its signature charming way BDB Theological Dictionary states the 'question intricate and conclusions dubious.'
The way we, here at Abarim Publications, understand it, is that the word el was either the common Canaanite word for god, or a specific deity named such. When the Elohimite cult was introduced in the region, the name Elohim was formed independent of the word el or name El. When the reference to the Israelite God Elohim needed to be abbreviated (to serve as an element in names, for instance), the result was a second word el or name El, which was indistinguishable from the first one.
It's probably a bit like when someone from Faroffstan named Itzenbil (means 'mighty worried but rarely frowning' in his native language) moves into your neighborhood. Soon people start calling him Bill (short for Itzenbil), which is indistinguishable from Bill (short for William) who had been your neighbor for decades.
Originally El was the name of a Canaanite god, but Biblically the name El stands to Elohim the way Bob stands to Robert.
Also note that the Hebrew name אל transliterated into Greek forms Ηλ, which constitutes the first syllable of the word ηλιος, (helios), meaning sun. This word comes from an ancient proto Indo-European root.