Basically you can't Sync.
You can Copy the catalog file, its associated Previews folder and "ALL" your images over to the Mac from the PC. Then Open that catalog file on the Mac.
Or Copy the catalog and previews folder to the Mac and place the images on an external drive.
With either option you will then need to Reconnect the catalog to the image files by using the Locate images system within LR. You'll need to do that because the catalog will be looking for the images on a drive with a Letter, C, D, E, Whatever, and Mac used Drive/Volume Names not Letters.
It is possible to keep two machines fully synchronized, I do that. But it requires file synchronization software. On Windows there is "SyncToy", freely downloadable from Microsoft, which is actually not a toy at all, but an excellent piece of software for this purpose.
Your problem, however, is crossing platforms. That complicates it, because for synchronization to work you need identical paths and folder structures.
With sync software, the Lightroom catalog is treated as a single file just like any other, and is copied as "modified" in its entirety. That makes a separate backup regime for the catalog a necessity, since any corruption would just propagate. But this is handled with the standard Lightroom backup.
The simplest way to set things up so that you can use the same catalog on both systems is to put the catalog and the photo files on a single external drive, which you then swap between systems as needed. If you set things up correctly, you can even avoid having to "relink" the photos every time you switch. You do that by having the photos stored in the same folder as the catalog and at the same level, e.g. say you have "yourname Catalog.lrcat" located in the root of a folder called "Lightroom Sync", so then you would need to have all your photos placed in the same "Lightroom Sync" folder, again in the root so that the photos sit at the same level as the catalog (sticking all the folders under a single parent folder at the catalog level is easiest). Setup like that, Lightroom can use the relative path from catalog to photos and so avoid any need to be concerned about the naming/lettering convention of the OS. Obviously, the hard drive would need to be formatted such that both Windows and OSX have read/write permissions on the drive, e.g. FAT32.
There are other, more complex, methods (such as using something like Dropbox), but the "all on one drive" method is by far the simplest (and probably safest).