Rapidly and differentially rotating compact stars are believed to be formed in binary neutron star merger events , according to both numerical simulations and the multi-messenger observation of GW170817 . Questions that have not been answered by the observation of GW170817 and remain open are whether or not a phase transition of strong interaction could happen during a binary neutron star merger event that forms a differentially rotating strange star as a remnant , as well as the possibility of having a binary strange star merger scenario . The lifetime and evolution of such a differentially rotating star , is tightly related to the observations in the post-merger phase . Various studies on the maximum mass of differentially rotating neutron stars have been done in the past , most of which assume the so-called j -const law as the rotation profile inside the star and consider only neutron star equations of state . In this paper , we extend the studies to strange star models , as well as to a new rotation profile model . Significant differences are found between differentially rotating strange stars and neutron stars , with both the j -const law and the new rotation profile model . A moderate differential rotation rate for neutron stars is found to be too large for strange stars , resulting in a rapid drop in the maximum mass as the differential rotation degree is increased further from \hat { A } \sim 2.0 , where \hat { A } is a parameter characterizing the differential rotation rate for j -const law . As a result the maximum mass of a differentially rotating self-bound star drops below the uniformly rotating mass shedding limit for a reasonable degree of differential rotation . The continuous transition to the toroidal sequence is also found to happen at a much smaller differential rotation rate and angular momentum than for neutron stars . In spite of those differences , \hat { A } -insensitive relation between the maximum mass for a given angular momentum is still found to hold , even for the new differential rotation law . Astrophysical consequences of these differences and how to distinguish between strange star and neutron star models with future observations are also discussed .