Sorry if this has been brought up earlier but what's the size of BS-11.1? I am confused because my 2015 MBP is showing the size of over 3GB where as my new MBP M1 is showing 4.19GB.
It's an incremental
delta update, only the relevant subset of the whole update. I guess there were more code changes between 11.0.1 and 11.1 from the M1's perspective, because it's a more recent piece of hardware. Recently written graphics drivers etc. could be getting more frequent updates for a while.
Some people don't trust incremental updates and choose to download a
combo update separately. That will update everything, even if it was already up to date. Whether it makes any difference, the evidence for that is anecdotal. Could be true, could in many cases be placebo.
However, it does reliably help in special cases, for instance if a previous update attempt has failed for some reason. Using a combo update will update everything, just in case. One should achieve the same result by downloading the full installer from the App Store.
With Big Sur it should be more rare to have a botched update, since the process is now different: it updates a
snapshot of the system volume, instead of the system volume itself, making it possible to revert to the pre-update system if anything goes wrong during the process. More info in Ars Technica
review.
If there's no problem, then don't try to fix it. Incremental updates should be OK, if the system is otherwise already behaving OK.
Edit: Based on the update sizes on
this page, it looks like your 2015 MBP downloaded the delta update, and the M1 chose to download the combo update, and perhaps also a new firmware.