We compare two types of Tsallis distribution, that is, with and without thermodynamical description, using the experimental data from the STAR, PHENIX, ALICE, and CMS Collaborations on the rapidity and energy dependence of the transverse momentum spectra in $p+p$ collisions. Both of them can fit the particle spectra well. We show that the Tsallis distribution with thermodynamical description gives lower temperatures than the ones without it. The extra factor $m_T$ (transverse mass) in the Tsallis distribution with thermodynamical description plays an important role in the discrepancies between the two types of Tsallis distribution. But for the heavy particles, the choice to use $m_T$ or $E_T$ (transverse energy) in the Tsallis distribution becomes more crucial.