The essential difference between the mechanisms is that in step polymerisation all the molecules are reactive, so until the late stages you are mainly getting reactions between monomers or low oligomers, e.g. AA reacts with BB to give A-B and then that can react with a monomer to give A--A or B--B etc. So you always have a relatively large number of relatively small molecules until near the end, when oligomers react to give polymeric molecules. In chain polymerisation, the monomers do not react with each other, only with activated molecules e.g. chains with a radical end. The predominant reaction is addition of monomers to a small number of growing polymer chains, with a small proportion of termination reactions. So the mixture, even at relatively low conversions, consists of polymer and unreacted monomer. Of course if you consider the whole mixture, including unreacted monomer, at low conversions the number-average molecular weight is relatively low, but if you just consider the polymer molecules (growing and terminated), their average MW can be high even at low conversion - but there are relatively few of them.