Bitcoin halving has always been confused for crypto burning most especially by those who are new to the crypto space. If not carefully looked at, Bitcoin ethusiast might even fall in the same situation the very moment the two words are mentioned.
I would start by saying: Bitcoin halving is practically a mechanism that helps to reduce/cut the rewards of miners, thereby reducing the amount of bitcoin entering into circulation.
While crypto burn is a mechanism use by other cryptocurrency in reducing the amount of their digital asset already in circulation.
You explained it well, but just to be frank, I doubt if any of the newbies would be confused in these two terms because they are so obvious but still, I presumed many things to be what they were not (when I was newbie) so I can say that there are newbies who think of both as same. It's good that you distinguish between them.
Even though, I doubt if any of the Bitcoin Enthusiast would be confused with these two terms.
There are many newbies (and experts) who think they know everything, for example, many don't know tokens and coins are not the same things in cryptocurrency. Even they are experts. Topics like these are good reminders for those who already know about it and good pieces of information (eye-opening) for those who take it wrong.
The two main phrases in both definition states the big difference between them. Halving helps to reduce what's entering into circulation, while burning helps to reduce what's already in circulation.
We should note that halving is an automated mechanism that would occur when every 210,000 blocks have been mined. It is practically used for bitcoin. While burning is intentionally done by the developers of that particular coin.
Well, just to clear things out, Halving was also implemented by the founder, which means, it is created or developed or integrated (whatever you can say) first in the BTC blockchain and then afterward it is programmed as automated and the burning could also be automated after implementing it first (intentionally). So, the difference of automation and manual seems not right.
Though, they both have little similarities such that: both mechanism helps to activate scarcity. After burning, there are possibilities that the specific coin would increase in price or not, but what do you expect when there is scarcity ?. The same goes for Bitcoin halving.
That's not what scarcity means in the context of BTC. Like in BTC supply is fixed but if you are burning some tokens (ALTS) then the supply can be changed there (means can be increased), other than this, burying and halving did reduce the supply in circulation and had a positive impact on the price, but nothing resembles BTC. Even the hard-forked BTC version which also follows the halving paths.