disk utility...

I would "trust" the one in Recovery Mode. Chances are there is something amiss with one of more of the drivers on your Mac that is giving you this error when you log in normally. One thing to try is to create a new user account. When booted up normally, log out of your existing account, and then, back in with this new one. Then run the Disk Utility. Does this error still occur? If not, then you narrowed it down to your existing account.

What were you trying to do that required that you needed to use the Disk Utility so that we can get a better idea on how to help here?

Disk Utility is a bit of a misleading term as it does not check the Disk it only checks the Disk directory, if it was testing the whole

disk it would take significantly longer. It does not check software or your files.

If you want to run First Aid and for Disk Utility to run any repairs then you can only do that when booted to your Recovery HD

when you open Disk Utility click on View in the menubar and select Show All Devices.

This will show you the device tree, with the Disk first and then the Container disk and then the Volume (Macintosh HD)

you can run Disk Utility on each if you want.

If Disk Utility gives you green tick for each then leave it there and get on using your mac.

Although you may find documentation on using Disk Utility, getting something that provides the details behind those "errors", AFAIK, it not available outside either Apple Engineering or the Apple Developer community.

Where I have seen these before related to corrupted Time Machine backups to local Snapshots on Mac drives formatted with APFS. These numbers relate to objects that are expected to be one value, but DU finds it to be another. In most cases, it can resolve them, but not always.

Going "outside the OS" is the only way Apple provides to fully test its internal boot drive for errors. Again, was there something going on that you needed to run the Disk Utility for? So far, all we know, is that you have a MacBook Pro running macOS Mojave.

I'm not sure I'm following your logic here, but whether you use Disk Utility (DU) in Recovery Mode or when booted up normally, it is software built into macOS. The DU is actually a GUI for the actual commands that you would have had to enter in the Terminal app if that GUI didn't exist. Its major function is to administer disk drives ... both internal to a Mac or directly attached to it. AFAIK, it doesn't directly determine issues with software. Indirectly, if it detect errors with a drive and an app happens to reside on that drive, that could be a cause of an app failing to function properly.

As far as "what the numbers represent in parenthesis" mean, you will need to provide either more details or a image capture of what you are referring to.