How to only back up one partition of a Macbook hard drive?
Your problem is a consequence of an over simplified vision of users from Apple:
a user has one uniq computer with one uniq partition then name it with a simple and uniq name "Macintosh HD".

Once you start to have external disks, different versions of OS on the same disk, you should carefully avoid all the failures this over simplistic naming scheme will led you to.

Change all your partitions names with a very clear and really unambiguous name
for you and forever.

My personnal use is as follows: every disk partition is named from the computer name it is used on ex.: coriolis, the partition number ex.: 1, its actual capacity, ex.: 250 Gb and the version of the OS it is used on, ex.: High Sierra for a production OS or 10.14.1 for a test one.

Ex.:

coriolis 1 250 Gb High Sierra
coriolis 2 250 Gb 10.14.1


All my computers, all my external disks have a different and uniq name registered at time of their 1st formatting.