Any updates come from Samsung -- that is a correct statement.
Pushing the "Check for updates" button tends to be more of a placebo thing. I've never had success in it returning anything besides "hey, you're up to date. yay."
They generally release in a staggered fashion. Not everyone gets the update at the same time -- otherwise, servers wouldn't be able to handle the demand. They usually do a small segment to make sure the update doesn't brick devices. Then, they add more and more until it's pretty much universal.
Back in the day, Samsung Kies would update your device if there was one available (whether or not your phone has been put in the aforementioned subset). Have you tried? (I'm assuming Kies is the proper PC software for it still).
My unprofessional opinion -- enjoy your phone as it is. There's probably nothing critical in the update that you absolutely need to have it now -- if there was, you'd be on a device that always is current-updated like the Pixel 2 .
FWIW, there's plenty of times I tapped on that "check for updates" link and got an update. For example, when updating to Oreo; when I had an S5, every blame update from Android 4.4 through 6.X and all the security updates inbetween came in that way.
Admittedly, if one doesn't do the tap and check, within some period of time or other it'll get announced and installed anyway. But I check once or week, being the manic type.