Ok, firstly lets not worry about the terms for now.
We can split movement across the membrane into 2 categories: energy requiring and no energy requiring.
For energy requiring movement, there is active transport and bulk transport. They are both transporting substances across the membrane, hence requiring energy. Bulk= large stuff, so transport of insoluable large substances. Active= wanting to move, hence moving against the gradient.
For no energy required movement, it is all just different types of diffusion. Simple diffusion = diffusion without intervention. facilitated diffusion= diffusion with help i.e. Through channel proteins or carrier proteins.
Osmosis is just diffusion of water through a semi permeable membrane btw.
Hope that helps. This is just a quick summary not an A+ definition of all thr terms