IIRC Neutrino can use a pruned Bitcoin node, and since it says "Neutrino based" i guess that would be logical, unless its bundling the whole thing.
The Lightning App is a Lightning Node (LND based). Neutrino negates the need for a bitcoin full node(for these use cases).
It is a Light Node that can be run on smaller devices. Basically it downloads a filtered version of the blockchain in a way that it can trustlessly check transaction info using 1/250th of the space, and without leaking any of the user's info like SPV does.
Initial sync is done in a few minutes in the background while you write down your seed, and each new block is represented by a filter of about 15kb. So very low bandwidth and storage requirements.