As far as I know those two models of quaternions are the same thing. The quaternions in these videos are (an awkward representation of) 3d rotation operators, u

As far as I know those two models of quaternions are the same thing. The quaternions in these videos are (an awkward representation of) 3d rotation operators, under the correspondence i = R_yz, j = R_zx, k = R_xy (although you can assign whichever axis to whichever quaternion you want, and you can arbitrarily swap i<>-i, j<>-j, k<>-k. From googling it looks like the JPL convention is to swap k<>-k, such that ij = -k instead of ij = k).