If you choose Run, the file is downloaded into a Temporary folder and then Run. It will perform the update.
If you choose Save, you need to specify a location on your hard drive to save it to. Then you need to go there and manually start the application to perform the update.
I prefer the latter because then I have it on my computer in case I need to reinstall AC and apply to hotfix again.
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2x28" (2560x1440), Windows 10 PRO ENG, Ac20-Ac28