  We consider the monomial expansion of the $q$-Whittaker and modified
Hall-Littlewood polynomialsarising from specialization of the modified
Macdonald polynomial. The two combinatorial formulas for the latter due to
Haglund, Haiman, and Loehr and Ayyer, Mandelshtam and Martin give rise to two
different parameterizing sets in each case. We produce bijections between the
parameterizing sets which preserve the content and major index statistics. We
identify the major index with the charge or cocharge of appropriate words and
use descriptions of the latter due to Lascoux-Sch$\ddot{\text{u}}$tzenberger
and Killpatrick to show that our bijections have the desired properties.
