Loeyrodeo is back and bio is forward. Rodeos 5's and flat 5's are similar, flat 5's are just more inverted. Bios are like forward corks (sort of) its an axis between straight up and horizontal.Though I can see how you are confused because sometimes it looks like people are pushing forward on rodeos.
Bio: https://www.youtube.com/watch?v=JlBiMXkvF78 (I know its a big spin but its a good example of the axis)
It all depends on the set of the trick, like some rodeos straight up look like some mistys, and then some rodeos look completely opposite from other mistys. Most ros i see nowadays are pushed liked you said, which is confusing af. Then there's flats as well that are pushed, especially flat5, like dam a flat5 bow n arrow can look like a bio.
I think the real difference is that on a flat/rodeo you push your back forward (if you set it not the classic way) first, whereas in a bio/misty you go head first then the back follows. Also, always look at the skis compared to the head right after the set to make out the trick, on rodeo/flat, the skis will will be level with head or higher (for rodeos especially). For misty/bio, the skis will be lower than head at first and come up as you invert (for a misty).
But yeah after the set, in spins bigger than 9 tricks can look like all sorts of other tricks.
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