What is ColorSync?
(confusing us) is My PEEVE!

ColorSync Utility to shrink PDF with custom filters from Preview Quartz Filter - colorsync-filters.md. ColorSync Utility Printer profiles missing on macOS: A permanent solution Many Mac users find that the ICC profiles for their printer stop appearing in applications such as Adobe Lightroom Classic and Adobe Photoshop.

ColorSync® is a registered trademark of Apple Computers.

'ColorSync Profile' = ICC Profile = 'ColorSpace'

ColorSync is — merely — a Color Management System (CMS - CMM). In the case of OS-X, ColorSync also includes an application 'ColorSync Utility.app' used to set up and repair ColorSync issues on the Mac. Adobe (ACE), Heidelberg, Agfa, and Kodak CMS/CMMs are also individual Color Management Systems (CMS), Color Management Modules (CMM).
The ColorSync Utility enables configuring color profiles to maintain color matching across multiple devices, applications, and when printing. Using the drop-down menu (the menu displays the Match.

I think the color confusion starts by using Apple's 'ColorSync' terminology to encompass 'color management':

ColorSync this..
ColorSync that..
ColorSync calibration..
ColorSync Profiles..

I will argue 'ColorSync Profile' is more accurately referred to as an 'ICC Profile' in the field of digital color management.

ColorSync is — merely — a Color Management System (CMS - CMM).
In the case of OS-X, ColorSync also includes an application 'ColorSync Utility.app' used to set up and repair ColorSync issues on the Mac.

Adobe (ACE), Heidelberg, Agfa, and Kodak CMS/CMMs are also individual Color Management Systems (CMS), Color Management Modules (CMM).

Read about BASIC THEORY HOW PROFILES WORK in color-managed applications.

See ColorSync ICC Profiles in action in your Safari, FireFox IE Web browsers.

Here is Apple'sReference Library ColorSync page at Apple.com.
For more on the ICCInternational Color Consortium www.color.org.

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LANGUAGE-TRANSLATION ANALOGY

Colorsync Utility

Think of any Color Management System (CMS) as an interpreter of ICC profiles.
The CMS can speak all ICC–profiled languages.

Think of any ICC profile as the written language of each individual, SPECIFIC DEVICE (or ColorSpace) it represents.

Think of your specific monitor ICC profile (MonitorRGB) as an English speaker.

Think of your specific printer/paper/ink ICC profile (TargetICC) as a Spanish speaker.

Think of your Photoshop TaggedFile as a Japanese speaker.

'TaggedFile' represents the Embedded/Tagged colorspace of the open RGB or CMYK file.
If you are Embedding/Tagging your RGB files with 'Adobe (1998) RGB' for example:
TaggedFile = AdobeRGB = WorkingRGB

Further: Enabled Monitor ICC Profile = MonitorRGB

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Think of what the Color Management System does:

MonitorRGB < TaggedFile > TargetICC/CMYK

In other words:
TaggedFile is CONVERTED to MonitorRGB.
TaggedFile is CONVERTED to a specific TargetICC or CMYK.

The CMS takes Photoshop's TaggedFile, Converts (translates) it into MonitorRGB (and onto the screen).

The CMS takes Photoshop's TaggedFile, Converts (translates) it into Specific printer/paper/ink ICC (and onto the print).

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Without an interpreter, a CMS — our eyes are explaining our color to an English speaker (MonitorRGB) who explains it to a Japanese speaker (TaggedFile) who explains it to a Spanish speaker (Specific printer/paper/ink) — a screen–to–print match is not gonna happen.

See embedded ICC Profiles in action Color Management tutorial
Includes on-line demonstrations of Tagged and UnTagged sRGB, AdobeRGB, AppleRGB
Monitor calibrating and profiling tips, 2.2 gamma, 1.8 Mac gamma, D65 6500 degrees Kelvin

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