Per What is the difference between regular and "twisted" ECC curves? I guess the brainpool twisted curves and the brainpool regular curves use the same point addition and point doubling algorithms.
Domain-parameters.pdf#page=15 mentions the parameters for the 160-bit regular curve and the 160-bit twisted curve. For the regular curve it has a $p$ parameter and for the twisted curve it has a $Z$ parameter. I assume the $Z$ parameter is the prime number you need to do the modulo of after every operation.
What about the order $q$? Is the order the same for both curves?
If the curves are the same thing then couldn't one just treat them as aliases of one another? Like when you're randomly selecting $k$, between [$1, n-1$] and then multiplying the base point by that then you'd get the same answer no matter which curve you used?