Size matters as does the range, but they are two different things, there are intermediate range missiles that carry nukes and American nukes have selectable yields with a maximum yield of 500KT right down to tactical nuke levels. So, what is a tactical nuke when they can have selectable yields? It is a distinction without a difference. How would one tell what kind of warhead would be on a short or intermediate range missile? Trust what Putin says?
Time to target is the biggest factor here and the Ukrainian border is only minutes away from Moscow and the Belarus border is minutes away from European capitals. Likewise with submarine launched intermediate range missiles that can be on target a few minutes after launch. It is the only advantage to placing nukes on the border, to reduce the range and time to target. If Vlad is gonna put nukes in Belarus, what would the targets be? NATO countries and if he is gonna fire one into NATO turf he might as well fire the lot and won't start with a tactical one. Tactical nukes are not very good against modern battlefield tactics where there are no large concentrations of troops, and it opens a pandora's box. NATO is not gonna attack Belarus, but it might fall to internal strife with outside backing and Ukrainian help. Russia proper is coming under attack with territorial incursions and drone strikes on Moscow and still no nukes yet.
I think it is just posturing and no nukes will end up in other countries, if they were used the Russians would get the blame anyway, just as if American nukes stationed in allied countries were used, America would take the heat for it.