there's a similar thread already if you want to do a search.
I'll briefly answer to the best of my ability, then feel free to join the existing threads that are already posted.
A shoulder bag is a purse/bag w/ a strap long enough to carry on your should.
Handbag is also called a purse sometimes - but would literally be a bag carried by hand, or maybe crook of your arm near elbow - strap not long enough to be carried on shoulder.
To me a satchel = tote - a biggish open bag usually carried on the shoulder.
I use bag/handbag/purse interchangeably.