There are lots of altcoins. Taking Litecoin as an example, an altcoin modifies the Bitcoin protocol in some way or other, starts over with a completely new ledger and a new name.
In contrast, there has been no fork of the Bitcoin network until now.
A fork changes some rules like an altcoin project. But it keeps the ledger and intends to keep the name.
The term “Bitcoin” has a lot of brand value. Therefore, the question of which chain gets to call itself “Bitcoin” after a fork is rather important.
The solution should be market based. List both coins on exchanges as Bitcoin1 and Bitcoin2. Wait for three months or some other suitable period of time agreed by both sides. Then award the Bitcoin brand to whatever coin has the higher valuation after that period runs out. The losing chain would need to use some other name.
If this can be done, this may be an excellent upgrade mechanism. Whenever there are serious differences of opinion on the way forward, fork the coin calling both Bitcoin for three months and let the market decide the winner.
Some people fear forks. I fear blocking progress more. Bitcoin must be able to innovate, and it needs a clear upgrade mechanism for that.