Hola Seokho espero estés muy bien, la primera oración es una forma indirecta de invitar siendo amable y cortes, mientras que en la segunda oración haces una invitación ya de manera directa y un poco informal, por lo general esta segunda oración la usamos con personas cercanas a nuestro circulo familiar o de amistades. Espero te sirva, un abrazo desde Ecuador

Hola Seokho. In the first sentence you're asking the person if He/She would like to have dinner at your home. But in the second case you're affirming that you both are going to have dinner at your home

La diferencia esta la siguiente: 1) si quieres, podemos cenar en mi casa => Estos es mas como una pregunta para la persona que esta invitando a cenar y es una manera mas formal. 2) si quieres,! Vamos a cenar en mi casa! => Esto es una invitación directa e informal (usualmente lo usaríamos con personas que tenemos mas confianza)

In the first sentence you are being polite, it is an indirect way to invite. In the second you are inviting the person directly.

Hey! they both mean the same but one is more enthusiastic than the other. "Vamos and podemos" are key to understad that. "Podemos" comes in like a question. Arguably, it could be stated that it leaves a certain kind of shyness. On the other hand, we have "vamos", which's a direct invitation to the other person. Again, this is arguably a more enthusiastic way to invite someone to have dinner. If you have any other doubt, please let me know!