the base wallet is just a rebranding of coinbase wallet. it's technically a self-custody wallet that supports seed phrases. it will pressure you into using an EVM network called Base which, despite being centralized, does inherit an acceptable amount of security from the ethereum network on account of being an OP stack rollup. it supports more networks as well. base wallet will also pressure you into using passkeys instead of seed phrases.

smart contracts and protocols that you interact with using wallets such as base are not guaranteed to be decentralized. but to be fair, the b*tcoin stuff like boltz isn't decentralized either. glass houses and that.