On-Chain ("normal" bitcoin) vs Off-Chain (lightning) transactions
Bitcoin has a scaling problem. You either have to wait a long time or spend a lot of money to send a transaction during busy times.
On-chain bitcoin transactions handle 7 per second. Visa can handle 65,000 per second.
Lightning network solves this by multi party smart contracts (programmable money) which uses Bitcoin's built in scripting.
Likely in the future, all wallets will support lightning and handle all of this behind the scenes and the wallet will automatically use whatever makes the most sense for the user.
Wallets
Desktop wallet used was Electrum (now supports lightning).