Magnetospheric convection, the transport of magnetic flux, along with mass, and energy, plays a vital role in magnetosphere‐ionosphere coupling and ring‐current energization. It is particularly intense during magnetic storms, a mode of circulation driven by prolonged and strong solar wind driving. A large body of work has quantified the evolution of flux circulation during nonstorm times, in particular during substorms and steady magnetospheric convection events (SMCs). However, transport during storms has not been duly characterized. Using magnetotail flux observations we explore storm‐time modes of convection and compare them to their nonstorm‐time counterparts. We find that storm‐time convection often encompasses loading‐unloading periods (akin to substorms) and SMCs (akin to those during nonstorm times). However, loading‐unloading events and SMCs are present during only 25% and 21% (respectively) of the (95) storms examined. We also investigate the solar wind conditions during these modes for storm versus nonstorm times. We find that these modes have characteristic profiles in AE, solar wind driving, and open flux content during storms that are similar to their nonstorm‐time counterparts, but larger in magnitude. Therefore, these convection modes occur during storm and nonstorm periods alike, and in particular they are not required for a storm to progress. Thus, what makes storms special, their intense ring current, is likely not attributable to the (un)steadiness of flux circulation, but to the prolonged and intense background flux circulation within which these modes are embedded, and hence to the ultimate strength of the solar wind driver.