After the great schism of 1054, when the east and west roman empires split religious beliefs, what two main groups were the result?

The Roman Catholic and the Eastern Orthodox faith.

The Great Schism of 1054 was a religious conflict between the western and eastern branches of the church. There were several issues that divided the church's opinion, such as the use of unleavened bread, the role of the Holy Ghost, and more importantly, the authority of the Bishop of Rome (the Pope). On July 16, 1054, the Patriarch of Constantinople Michael Cerularius was excommunicated, effectively leading to the schism.

explanati“there were many such dangers, in which the odds were all against them. their children were not as well as they had been at home; but how could they know that there was no sewer to their house, and that the drainage of fifteen years was in a cesspool under it? how could they know that the pale-blue milk that they bought around the corner was watered, and doctored with formaldehyde besides? when the children were not well at home, teta elzbieta would gather herbs and cure them; now she was obliged to go to the drugstore and buy extracts–and how was she to know that they were all adulterated? how could they find out that their tea and coffee, their sugar and flour, had been doctored; that their canned peas had been colored with copper salts, and their fruit jams with aniline dyes? and even if they had known it, what good would it have done them, since there was no place within miles of them where any other sort was to be had? the bitter winter was coming, and they had to save money to get more clothing and bedding; but it would not matter in the least how much they saved, they could not get anything to keep them warm. all the clothing that was to be had in the stores was made of cotton and shoddy, which is made by tearing old clothes to pieces and weaving the fiber again. if they paid higher prices, they might get frills and fanciness, or be cheated; but genuine quality they could not obtain for love nor moneyon: