Genesis 1:1-2:3 is a poem of the first seven days. It is a broad overview of creation. Chapter 2:4 begins the narrative of the relationship between God and humanity. The style, language, and purpose of chapter 1 is different than chapter 2. Chapter 1 presents God in His transcendency decreeing each element of creation, recorded in a memorable form. Chapter 2 presents God as imminent and intimate with His creation. Chapter one talks about what Elohim did. This is the general name for God, morphologically related to Allah, and akin to saying "man". Chapter two introduces God as Yahweh Elohim. This is God's personal name. It means (in answer to your question) "I am". It's like saying, "You were created, but I just am." So, the differences in one and two have to do with style, language, and intent.
But going back to the name of God for a minute, the Hebrew language has no vowels. It's a completely consonantal language. The name Yahweh is actually just four letters: YHWH. The oldest copy of this name we have was found by Gabriel Barkay at the Temple Mount dig. It's a small silver scroll which dates back to 600BC. It's a copy of the priestly blessing found in Numbers 6 ("May YWHW bless you and keep you...") so we have that from at least 600 years before Christ.
As language developed it began as completely pictorial. A picture of an ox represented an ox. A picture of a camel represented a camel. Over time these pictures became codified so that the picture of the ox was drawn the same way every time. As more time passed the pictures became letters representing sounds, but the letters kept the meaning they originally had.
For instance, the first letter of the Hebrew alphabet is alef, meaning ox. Then comes beth (house), gimel (camel), dalet (door), and so on.
So the intimate name of God is YHWH. In the minds of ancient Hebrews the letters that were used to make up a word had significance. So let's look at the letters the make up God's personal name. Y is yod. Yod means hand. Next is H. H is he (pronounced "hey"), which originally meant window. Over time the word meaning changed to Behold!, like an exclamation. It's not to hard to see the correlation between window and Behold!, and still we use H that same way ("Hey! Come here!"). So Y is hand, and H is Behold! But what about W? W means nail. When we read the ancient name of God the way the ancients would have you get "Behold the hand! Behold the nail!"
