Wood – Why does the circular saw shaft spin and blade does not

Make a shim out of thin cardboard and place it between the inner blade washer and the blade. The blades they're making these days are thinner than the older blades and some of the older saws have to be shimmed in order to prevent blade slippage.

Jig saws are for delicate work; they cut slow and the blades like to bend and break.

Reciprocating saws are for not delicate work and cut fast, the blades bend if you let the tip of the blade bounce on your work.

Circular saws are for relatively straight cuts, their blades do not break or bend, readily.

Table saws are just better circular saws.

Miter saws are for nice, straight cut-offs.

If I had to pick one to keep, it'd be my real (Milwaukee) Sawzall®. In a $50 price range you can get a crappy jig or reciprocating saw. For chores around the house (random home improvements) get a reciprocating saw. For small wood working projects, you may want a jig. I 'work with my hands' and to me a jig is a specialty tool, seldom necessary and a pain to keep changing blades and they take forever to cut.