The P-360's are an 8-way that uses optics, rather than conventional switches, to detect movement of the stick.
The top half is very similar to a normal Happs stick; but the actuator doesn't contact anything on the bottom, so the stick swings around in circles with no corners--thus the name PERFECT 360.
The advantages to the optic system are no clicking, no corner hangups anywhere, and no mechanical wear from switches being contacted.
They are NOT like an analog stick, in that they don't send data based on how FAR they are moved from center.
That is where the 49 way sticks come in.
The 49-ways are very similar in operation to the P-360, but have more sensors in them.
The P-360 is uses a 3x3 matrix, so it detects the stick as either right/center/left and up/center/down.
The 49 way is a 7x7 matrix, and detects up3/up2/up1/center/down1/down2/down3 and left3/left2/left1/center/right1/right2/right3.
This allows the 49-way stick to function as an analog stick with a proper adapter.
TRUE analog sticks use a 256x256 matrix, so the 49-way, though similar, is not as precise.