With 1.44MB disks, you are instructed to shut down the computer, boot
from the first floppy Install disk, and follow the installation program
from there.
The installation using 800K media is slightly different. You're
instructed to insert the first floppy Install disk while the Macintosh
is running, and follow the installation program from there.
There are no problems using 800K media in high density floppy disk
drives. The key difference is that you can't start up the Macintosh
with System 7.1 on 800K disks. The 800K Install disk doesn't have room
for the system files required to start up a Macintosh.
The documentation in the System 7.1 Upgrade Kit is correct for 800K
media. The manual instructs users to insert the Install disk and
proceed from there. You shouldn't shut down the computer, and try to
boot from the disk.
Complete instructions for a Clean Install of System 7.1 are available
in a separate article in the Tech Info Library or from the FaxInfo
System.