LIT is a lightning network implementation separate from LND/Eclair (Bolt Family) so it differs in the way its built. Instead of having a bunch of different different lightning networks, one for each coin, LIT implements all the coins into a single protocol making a single unified multicoin lightning network, rather than a fragmented subset of lightning networks. LIT is headed by Tadge Dryja the co-author of the Lightning Network whitepaper at MIT-DCI.
Crypto App is a Vertcoin project. The box takes care of all the hard parts about Cryptocurrency, lightning transactions or on-chain transactions and abstracts it all into a simple user interface controlled via your phone. It turns out to be pretty similar to the fiat banking/card payment system we all know and love today, but with crypto.
Every part to this system is widely available, and can be assembled by the user. It also creates business opporunities for businesses who want to assemble and sell their own 'Crypto Boxes' and 'Crypto Terminals'. This system forms the basis for payment system infrastructure that can scale & match the current UX of the fiat payment system. This system also acts as a full node / lightning node, so it ensures as many people as possible are running full nodes and also enforces crypto transfer best practices. Users are always in control of their private keys at all times. This system runs on the LIT Lightning Network. Hybrid Terminals that accept both Fiat and Crypto style payments are also feasible, the possibilities are in your hands. Currently the main focus is on LIT, the lightning network that makes this multicoin approach possible which you can follow the progress on through Github.
Vertcoin runs as close as possible to Cryptocurrency fundamentals, the whole “be your own bank” movement that started cryptocurrency to begin with. Vertcoin is chasing something entirely different from the ICO/Premine groups. We just want to change the financial system for the better.
tldr: Long-term consensus distribution using GPUs & leading layer two solution innovation.