AIUI, grub consists of two parts. Stage 1 is placed in the MBR of a disk or partition, stage 2 is somewhere on disk.

It's the BIOS that determines which MBR is loaded, from there on, it is Grub.

Grub's stage 1 has to store, somewhere in the MBR, where stage 2 is. Stage 2 has to store, somewhere on disk, where the kernel, the initrd, and the root partition is.

The question is, how are these stored?

Does stage 1 record the disk by ID, or by device number?

Suppose I have a slave IDE disk I'm configuring to be my primary boot drive. It's currently /dev/hdb, and stage2 is in /dev/hdb1. If I write stage1 to the MBR, telling it to find stage 2 on /dev/hdb1, will it be able to do so, when I swap the drive jumpers, and that drive is now /dev/hda?

Off hand, I don't know the answer how grub part1 access the rest of grub. However, once grub is loaded, it has support to access the drives and partitions by name. It loads in the /boot/grub/menu.lst file to bring up your grub menu. This text file contains the location of the kernel and initrd file as well as other options. If it can't find it, you can enter the grub shell and locate them manually. It even has autocompetion which can help to browse the different partitions to locate where the kernel and initrd files are. From there you can enter the "b" command to boot.

If the bios and grub have different ideas on which is the first drive, you can modify the /boot/grub/device.map file to map /dev/sd* to (hd*) styled entries. This allows you to edit the menu.lst file, run grub-install and have the grub bootstrap loader installed to the correct drive.