Both do use AK pattern guns, with main caliber being 5.45×39, though Ukraine isn’t using them exclusively.
Current standard Russian issue rifle is the Kalashnikov AK-12, which is a modernized iteration of the AK-74, itself a variant of the AK rifle chambered in 5.45×39. This one has better sights, top mounting rail, foldable stock, etc:
Ukraine is less consistent. Its been trying to get away from Kalashnikov pattern guns, in part just for symbolic reasons, but also to go to NATO standard. Right now, I think its more tolerant of “use whatever we can get” so individual soldiers may be using non standard guns.
Its got plenty of AK-74 rifles still in service, but its also has other AK pattern guns, including individual AK-12 rifles its captured from Russians, and older AKM guns in 7.62×39. Its also got some AR-15 pattern and other rifles in both NATO standard 5.56×45, but also 5.45×39.
Reportedly some Ukrainian special forces are carrying Fort-221 rifles, which are licensed copies of Israeli Tavor rifles in 5.54×39:
Civilian/export version of Ukranian UAR-15, which is domestic version of AR15. There was some talk of Ukraine adopting this, but I don’t think its happened yet.
Interestingly some of the older Mosin-Nagant bolt action rifles have seen some field use on both sides mostly out of expedience. They’re available, the 7.62x54R ammo is available (its still commonly used for machine guns), and these are modifiable into passable designated marksman/sniper rifles: