Mac book software update downloads from apple.com Vs. Mac book automatically downloading them.

if I have an older Mac book that apple support says can no longer receive the new updates, can I download these updates on my safari and then get my computer up to date that way? from the downloads section off apple.com for MacOS.

what is the difference from downloading on safari @ apple.com/downloads Vs them automatically coming up under the software update in setting? this Mac book was a gift so for it not to receive the updates is frustrating would love any input anyone knows. thank you