Essentially, different types of network addressing. You send and receive packets of data (think like electronic ‘letters’ containing a certain amount of information) and the way those are addressed and the information stored in the headers (think like the front of the envelope) changes between IPv4 and IPv6.
IPv6 is a new(er) protocol that is being gradually introduced, because there’s an addressing problem where ipv4 was given an address field of 32 bits, which at the time was thought to be pleeenty. 2^32 equals about 4-odd billion combinations, which they’d thought would be hilariously more than enough when the protocol was designed. I mean, even if every village had a computer, we’d still have leftovers…
So, yes, once we all had three phones, five laptops, six desktops and our fridge, microwave and washing machine also connected to the internet, whoops, we have a problem. So, the critical driving influence for introducing IPv6 is that it has an address field of 2^128 = 340,282,366,920,938,463,463,374,607,431,768,211,456 possibilities.
Hopefully that will hold us for a while. On the other hand, people are currently researching paints where every particle of paint contains a tiny internet-linked sensor, soooo…we’ll see.
There’s all kinds of features and details beyond that, but it has even less to do with your problem than what I’ve already said. Crucially, the reason why your router tries both is that it’s backward compatible with IPv4 because much of the internet is still not updated to use IPv6, and we have all kinds of cheaty techniques to get around that for the moment. In principle, there’s no real loss to only connecting via IPv6, but it’s probably that something in your automatic settings is either causing hassle with IPv4, or your local DHCP server (the server in your region which dynamically distributes IPs) is having some problems with that protocol which they’ll solve themselves.
In any case, there’s no real benefit to connecting via IPv6. From your perspective, the experience is identical. The actual benefits are back-end efficiency which matter to your ISP and the internet backbone.