Disk utility detecting error in single user mode, but not when disk utility is opened via recovery mode
Here's a beginner's guide to the command line. The single user mode is also like looking in as root - the first user that owns all of the computer historically from a unix perspective.

the $ indicates a prompt where you, the human user can type commands. The system is telling you how to prepare the drive for running the repair command.

Type the following text - the same as the first line you are told to from the screen:

/usr/sbin/fsck -fy


Note, that every space, every punctuation is exact and changing any one item may run an entirely different command. If the fsck command has any errors, you can and should run it again with the same command up to three times in a row or more in some rare cases.

To get out of that screen, you could halt the Mac or type exit to resume the normal start up process.

Apple documents the root user and fsck in these two articles if you are curious or wish to learn more:


https://support.apple.com/en-us/HT204012 - About the root user
https://support.apple.com/en-us/HT201639 - Using Disk Utility and fsck
https://support.apple.com/kb/PH21893 - Single user mode in El Capitan