"Left and right pages are different because the margin has to be different for binding.
Chapter 1 ended on an even page (a "left page.") I inserted a Section break at the bottom of that even-numbered page hoping to start a new section on the next page (odd numbered), and change the header to Chapter 2. "
For the specifications above, the Inspector settings for Section 2 should be as shown in the image below:
Section break at the end of the text for Chapter 1. If you have "Section starts on" set to "Right Page" your next section will start on the first recto page after the section break, inserting a blank page if necessary. You can also set this menu (red arrow) to start the next section on Any page (it will start on the next available page) or the next Left page (it will start on the lext verso page—an unusual setting).
Page numbers may "Coontinue from previous section" or may re-start for this section, beginning with a value you set in the box (purple arrow).
Left and Right are different (green arrow) allows a different header or footer on facing pages (eg. Book Title on verso, Chapter title and page number on recto). Note that this setting does not change 'Right' and 'Left' margin options to "Inside" and "Outside." That change is made by checking the Facing Pages checkbox in the Document Inspector.
Finally, unchecking 'Use Previous headers & footers" allows editing the headers and footers in one section without changing those for the previous section. Note that the edits will take effect in the section containing the insertion point when the edit is made.