It is both decentralized and distributed. It's not P2P though, it's a hub-and-spokes architecture with several interconnected (federated) hubs.
Hubs can have decent uptime and thick internet connections. Hubs are relatively few so they replicate state quickly between themselves, and then more locally between spokes when they come online.
Most natural structures are more tree-form, like that.
That just depends on how you define "distributed". If it means "running on multiple machines", then even centralized protocols are distributed, since a part of the computation is running on your computer.
In context of protocols like Mastodon, if the end-user devices aren't primary holders of data, then I don't call it distributed. It's just decentralized. I guess that way, "distributed" necessarily implies peer-to-peer.
Mastodon is decentralized, because there is no central server. However, it is not distributed.