You need to use Metadata > Save Metadata to Files and Read Metadata from Files to move work by xmp, but remember that xmp doesn't contain all your Lightroom work and you'll soon be messing around moving lots of xmp files around into different folders.
A better way is to use File > Export as Catalog to take a mini catalogue from one machine, and File > Import from Another Catalog to bring it into the catalogue on the other machine.
Or put your catalogue on an external hard drive and move the drive between machines. That's probably best it you do this a lot.
Thank you so much for responding, John. I failed to include that I do use an external hard drive, and my files have been converted to DNG. I have moved files from one computer to another before and the new edits were always transferred with it. I must have made some change in presets, and I can't find it.
Is it somewhere in the catalog settings?
As John said, the best method is to create a mini catalog on one machine and use that to transfer to the other computer.
Working with DNG files still has the drawback that some of your work cannot be transferred that way.
Or you could check the option to Auto write changes into XMP.
Even with your images on an external drive, and even with the above option checked, some edits and or options you choose in LR are saved to the catalog file. So unless you move the catalog from system to system you might lose something. You could place the catalog on the external drive also. That way you would take everything from system to system.
Thank you all for the info. I haven't had a chance to work with it yet, but i so appreciate your responses!