hayah - translated "I Am"; means to be, to exist"Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am." John 8:58
egō eimi - translated "I am"; means I be or exist.The following is an excerpt from Henry Law's "I AM that I AM" sermon.
'I AM THAT I AM.' Here the first sound is eternity. Jesus, as God, here puts on eternity as His robe. He knows no past. He knows no future. He lives unmoved in one unmoving present. He stretches through all the ages which are gone and which are yet to come. His only bounds are immeasurable boundlessness. Before time was born, He is 'I AM THAT I AM.' When time shall have expired, He still is 'I AM THAT I AM.' If there had been the moment when His being dawned, His name would be, 'I am what I was not.' If there could be a moment when His being must have end, His name would be, 'I am what I shall not be.' But He is, 'I AM THAT I AM.' Thus He treads first and last beneath His feet. He sits on the unbroken circumference of existence, as He who ever was, and ever is, and ever shall be. Let thought fly back, until in weariness it faint; let it look onward until all vision fail; it ever finds Him the same 'I AM.'...