what is different between normal wallet and lighting ?
A standard bitcoin wallet is for receiving bitcoin on the blockchain itself while lightning is a payment layer that is for receiving payments much quicker, cheaper, and often with more privacy but it does have a bit of a learning curve. It may be best to focus on learning how on-chain payments work and then spend some time learning about payment channels and how they work.
I got someone who send me money thro lighting wallet which is another address ? isn't the same ?
A lightning invoice is much different than a bitcoin address because it contains a lot more information and has to meet certain requirements like an exact invoice amount.
You can send between lightning and on chain but you will have to pay the miner fee (which is low atm) and not all wallets support this.