You seem to have a reading comprehension impairment. Chapter 1 is an executive summary showing the general chronological order of creation. Chapter 2 goes into detail about the creation of Adam and Eve.
No, Gen 1:1-2:3 and Gen 2:4 on are different stories as is obvious to any reader who, as I put it above, has not since childhood been exposed to harmonising accounts. The general chronological order in the 2nd account (Gen 2:4 ...) completely contradicts the order of the 1st. In the first (as it appears in the text, but probably also the more recent) account life is created in this order: plants (Gen 1:11); fish & birds (Gen 1:20); land animals (Gen 1:24); humans both male and female (Gen 1:26-27). The 2nd account, but contrast, has this order, male human (Gen 2:7); plants (Gen 2:9); land animals & birds (Gen 2:19) and female human (Gen 2:22). Nor does the strict classification of creation by days in the 1st account, and the narrative necessity for the primacy of Adam and the final creation of Eve in the 2nd allow for any honest harmonisation of these two distinct accounts. I'm sorry you have been misled.
Now I could point out the differences style, the designed symmetrical account in the 1st account vs. the rambling folk-talesy tone of the second; or between the nature of God (Elohim), who creates by pure will, "Let there be light" and who dwells on high, with the LORD (YHVH ... for the fist few instances the harmonising YHVH-Elohim), a terrestrial being who "fashions" out of clay, who has to call Adam and Eve from their hiding spots and discovers their transgression by their covering (hardly behaviour God on high would engage in). But given the radical disagreement in the "chronological order of creation," all that would be superfluous.
See the heading at verse 4, Chapter 2?
And extremely interesting verse. Though there is room for disagreement here, the best reading IMO is that this verse, though presented as a way to connect both accounts, the first half of the verse "[t]his is the account of the heavens and the earth when they were created" ends the first account, and the second "when the Lord God made the earth and the heavens" (a mirror of the beginning of the first, "When God began creating the heavens and earth ..." or however you want to translate this difficult piece of Hebrew). Among the facts that recommend this reading is the order heaven-earth vs the earth-heaven which reflect the extra-terrestrial and terrestrial nature of the different numen described above. Also that the highly symmetrical 1st account will end as it began. However, it may simply be that the entire verse is the introduction to the 2nd account.
I have only the slightest hope that this may help rectify your "reading comprehension impairment."