We study the connection of the high-frequency Floquet theory (HFFT) and the wave-packet dynamics (WPD) descriptions of laser-atom interactions. The analysis is motivated by the need to ascertain the realm of validity of the current form of the HFFT and extend its scope. We test the general ideas on a one-dimensional atomic model with soft Coulomb potential, frequently considered before. The comparison is carried out in two stages of approximation. In the first stage, we compare WPD predictions for ionization with those from the usual (single-state) form of the HFFT. To make the comparison meaningful, we use as initial conditions for the WPD bound high-frequency "dressed states," corresponding to the peak intensity of the field. The dressed states play a special role in the HFFT and have direct physical interpretation at high frequencies. We show that, under certain conditions, the decay rates extracted from WPD agree rather well with those from the HFFT. Thus "adiabatic stabilization," derived originally from the HFFT, results also from WPD. This form of the phenomenon contrasts "dynamic stabilization," the only form shown so far to follow from WPD. In the next stage of the comparison, we extend the HFFT in two directions: we include results from the second iteration within the theory, and we introduce a multistate HFFT analysis. As a test for the agreement of the HFFT and WPD we compare the results regarding the populations in dressed states. In a variety of circumstances we find striking agreement, indicating the potential of the multistate Floquet analysis. In addition, we study the characteristics of the population trading among the dressed states during the ionization process. Although the individual populations in bound states may fluctuate substantially, their sum decreases rather smoothly in time, as predicted analytically by the HFFT.