"We are inviting you to our house."
Translation:Zapraszamy cię do naszego domu.
They are both genitive=accusative of Ty, but Cię is not accented, and Ciebie is accented At the beginning of the sentence and after preposition it has to be Ciebie, in longer sentence if preposition is at the end it is accented, so also ciebie (and by longer I mean sentences when you can put ciebie in the middle). If cię/ciebie is in the middle of sentence you can use either, but cię is not accented and ciebie is accented.
this happens with all prepositions that have more versions in the same case. (he/she/it/they have third n+ version that are used after prepositions)