Creating iOS-like settings screen

The above answer is correct, but I wanted to add the solution itself here to save time for future users.
In order to make a regular UITableView look like the "Settings" page, you only need to to two things:
1. implement tableView(_ tableView: UITableView, numberOfRowsInSection section: Int) -> Int and tableView(_ tableView: UITableView, titleForHeaderInSection section: Int) -> String? so that the table will have multiple sections with headers.
2. set the table style to .grouped, which can be done via the storyboard editor.

Like 'Epic Byte' stated above, going with a UITableViewController with grouped style is an approach that ended up working for me. That tip put me down the right path.

Here are some links that helped me get the job done (in my case I also needed this to appear in a tab bar controller):

• http://useyourloaf.com/blog/static-table-views-with-storyboards.html
• http://www.appcoda.com/storyboard-tutorial-create-tab-bar-controller-and-web-view/
• http://shrikar.com/xcode-6-tutorial-grouped-uitableview/

Note that even though the screenshots appear to be for iOS versions < 8, the mechanics in the storyboard view carry over.