I think the differences between, say the Dominicians and Cistercians, are subtler and more of a 'spirit' or emphasis. Mass is fairly uniform within the Roman Catholic rite, but (and here my hinted at ignorance is now laid bare) one order may have a focus on charitable work, or education, or contemplative prayer, education or health....

Your faith as a Dominican or a Cistercian will be incredibly similar - Mass will essentially look the same, though the style of music chosen may be different, but the way you live out that faith will differ slightly. I'm sure all will value contemplative prayer, but for some it's a bigger part of their spiritual practice; all will honour and adore Mary but for some she will be a bigger source of inspiration for how they follow God's call in their life. All agree charitable works are important and some orders devote their life to them while others live out their faith by educating people.

I can only, inadequately, comment on the Roman Catholic rite (far left on on chart) and I hope others here will correct my errors. But as for the other orders on the chart, such as Orthodox, I have even less knowledge. I know at the heart they're Catholic but some of their beliefs and a lot of their ways of practising their beliefs are very noticeably different to the Roman Catholic rite, and as a Roman Catholic we are not meant to receive communion in their Masses (unless there are no Roman Catholic options, I think???), as we are not in full communion of beliefs with each other.