Before you start
Preview saves your changes as you make them. To keep a PDF as it was, open it in Preview and choose File › Duplicate first, then work on the copy.
In Preview, a whole PDF at once
Open the first PDF in Preview and choose View › Thumbnails to show its pages in the sidebar. Then drag the other PDF’s icon from Finder into the sidebar. Drop it at the end, or between two pages.
In Preview, page by page
Open both PDFs in Preview and choose View › Thumbnails in each. Drag the pages you want from one sidebar into the other. To choose pages that aren’t next to each other, hold ⌘ and click each one.
To change the order, drag the thumbnails up or down in the sidebar.
In Finder, with a Quick Action
Select the PDFs in Finder or on the desktop, Control-click them, and choose Quick Actions › Create PDF. Your Mac makes one PDF, named like the first file you selected. The files go in the order you selected them, so click them in the order you want.
The same Create PDF button is at the bottom of the Preview pane in a Finder window. If you don’t see the pane, choose View › Show Preview.
By dropping them on the notch, with Tilora
With Tilora, select the PDFs and drag them to the top of the screen. The notch opens into four places: the Shelf, Transform, iCloud Drive and AirDrop. Drop them on Transform and choose Merge PDFs. The new PDF is saved beside the originals, which stay as they were, and goes on the Shelf, ready to drag where it’s going.
It all happens on your Mac, with the Mac’s own frameworks; nothing is uploaded. More about the file shelf.
Not at your own Mac? Tilora’s free PDF merger works in any browser, and the files never leave the device you’re on.
Questions
Does merging change my original PDFs?
In Preview, the PDF you add pages to is saved with them, so duplicate it first if you want to keep it. Create PDF in Finder and Tilora both make a new file and leave the originals as they were.
Can I merge pictures into a PDF too?
In Tilora, yes: drop the pictures on Transform and choose Make PDF. Create PDF in Finder also combines the files you select into one PDF.