What is the difference between 44w and 1020 steel?

There may be no difference at all. In structural steel, 44W is a perfornamce rating (minimum yield strength 44,000psi). 1020 is steel chemistry (non-alloyed steel with 2.0% carbon). Quite often 44W is 1018 (1.8% carbon) or 1020 in composition. If your steel dealer is selling you 44W, ask about the composition.