Proof of work is a distributed random selection algorithm, or, as I often say, a lottery. But what makes it so there can be total agreement is the magic spice that Satoshi brought, the notion of hash weight as a discriminator for concurrent solutions.

Nodes keep the abortive offshoots that fork here and there as the inevitable sub-12 second concurrent solution discovery always makes the odd side branch.

Yes, indeed, you could say that nakamoto consensus is not a blockchain but more like a vine, with a central leader and small and short branches like the spiral grabbers on grapes or passionfruit. A block-vine. I don't think it will stick, but blocktree sorta sounds cool and it's almost valid, if you can call it a tree when it cannot grow laterally.