First off...
ACRONYMS
This is probably going to be the hardest thing to understand in this whole ordeal.
The letters.
SD = Spin Dash (Hop) (Side-B)
SC = Spin Charge (Down-B)
SDR = Spin Dash Roll (the 'rolling attack' part of the move when it reaches the ground)
SDJ = Spin Dash Jump (jump attack that can be done out of a SDR)
ASC = Aerial Spin Charge (air Down-B)
Throughout this thread, I'll try to keep the color coding the same so you can associate them better.
Yellow is for side-B,
Orange is for down-B.
Light blue is for the ground part (it's the same for both moves!), and
Dark Blue is the jumping part (same for both moves!)
Phases
You may have noticed that both moves roll, and both Side-B and Down-B can jump after the roll. Well, this is because the roll is actually the same move! Both the Side B and the Down B undergo 'phase changes', where they change 'moves' depending on where they are and what their previous phase was.
NOTE: "Charging" is a phase that is pretty obvious, but will be omitted here. More information will be found in the Move Properties section.
This maps out all the possible 'phases' that the move goes through during and after you release the charge. If you have a double jump, you can jump to cancel any of the aerial phases. Hitting
[Up],
[Jump], or
[Attack] out of the grounded phases (charge, SDR) makes you go into the spindash jump (SDJ).
Note: If a SDR goes to the edge of a platform, it becomes an ASC and assumes its properties. This means that even a Side-B Hop can turn into an ASC as long as you let it roll into the floor first.