Weird. My locally installed forum on my PC sees that the update is available but on my production one, the Administration center does not say an update is available. It also does not show the latest message in the "Live from Simple Machines forum" section about SMF 2.0.2 being available, just the SMF 2.0.1 and earlier messages. Hmmm..
Well, I uploaded the 2.0.2 patch file manually and installed it via the Package Manager. I still wonder why my local installation sees the 2.0.2 message in the Admin area and the installation at my webhost does not. Bizarre. It's like my server and SMF's server aren't on speaking terms for some reason.
I figured it out. The Fetch Simple Machines Files
task failed this morning. I saw it in my error log. I manually ran the task and now I see the updated postings about 2.0.2. I may need to adjust the time of day it does these checks as it seems to correspond with a lot of other server maintenance tasks at my host. At least I know what happened now.