WD Elements SE

Britney, if you formatted the drive as Mac OS Extended (Journaled) there will be no need to reformat the drive.

So you want to use the new WD drive on which you have already installed High Sierra -- at least that is what I think you mean when you say "formatted it to" -- as a backup drive for your Time Machine snapshots, right? Well, due to the way in which Time Machine works -- it keeps creating more and more snapshots until the drive is full, and then begins to thin the older snapshots -- if you want to save anything that is currently on that WD external drive, I would think that you have to partition it, so that you keep what you already have on there, but use a second partition for Time Machine's snapshots. I assume that Time Machine can do that; that is, just use a partition on the WD as its target, instead of the entire drive. I don't use Time Machine, so I could be wrong about this.

If you partition it, and the one partition is a bootable drive with High Sierra on it, then yes, you will be able to boot into High Sierra on it. Just don't use that partition to backup your internal Mojave drive. When you partition a drive, it is like creating two separate drives in one. What happens on one, will not affect the other. As to the other partition -- the Time Machine one -- well, obviously, it will be used entirely for your Time Machine backups. As I said, Time Machine will fill it up with snapshots, and then begin to thin older snapshots when the partition becomes full. This is all based on my understanding that you can use just a partition for Time Machine backup snapshots, and don't necessarily require a full hard drive for this purpose. If I am wrong, I am sure that someone else will point it out. :)

Is your intention to use the new WD drive as a backup drive -- Time Machine, CCC or whatever -- for your internal drive?

As for Time Machine, whatever your intent it, just note the Day and Time of the backup, as way to refer which OS backup it pertains to.