Artwork typically shows soldiers of the Kipchak Khanate of the time as equipped similarly to Timur's forces: the same styles of helmets, composite bows, steppe sabres, spears/lances, and round shields. Where armour is shown, it is similar (mail and lamellar). Whether there might have been a significant difference in the frequency with which armour was worn isn't clear from the artwork.

The major contemporary sources (e.g., the al Yazdi biography of Timur) don't note any differences in battlefield tactics. The overall impression from the sources is of two very similar armies fighting each other.

Al Yazdi does note that Toqtamish's army included forces from a wide variety of subjects, such as Russians, Circassians, Crimeans, Bulgars (Volga Bulgars), and Muscovites. This may well have resulted in some minor differences in the armies, but no impact on the fighting is noted in the texts.

The fighting is described in vol 1 of Pétis de la Croix's translation of al Yazdi's biography: https://archive.org/details/TheHistoryOfTimurBec_201409 (see, e.g., pg 318, or search the full text for "Tocatmich").