Ugaldie,i was born and grew up in Moscow,and have grown reading books much like these,and as good as the illustrators used to be(and they were excellent),they often didn't scruple to use their imagination...Personally,i don't recognise any of the axes pictured...
(Funny that being fluent in Russian i can't speak a word of Ukrainian,or Polish,or Serbian,or Any of the other Slavic language...(all of which can fairly easily understand one another).This right here tells a lot about how limited the Moscovy culture really was...
Yes sir,there Were other types of axes.Some were not massively different,but some were,indeed,fairly distinct.I'll try to find some good,representative photos.
As far as splitting goes,i believe that like in many other countries the use of saws by the poor peasants was not very common.Like that old English saying goes:"By hook or by crook",meaning that the landless peasantry were forbidden to cut any trees down,but were only allowed to gather the fallen branches,or the dead ones that they could pull down off the standing tree by a "crook".
So that they mostly burned small stuff.
Later,the last century or so,well into the Industrial age,there was a dedicated splitting-maul type axe(very crude and inconvenient to use to this day).
Wood was processed mostly by axe,and split by a warn out one,and then split further as necessary by a so-called "soven",a very thick/long knife-like object with a socket-like handle(like an unhandled British bill-hook).Like for splitting birch very small,to use in a special holder as about the only light source,or for stove kindling.
(Russian stove,a very specialised masonry affair,also used very small stuff as fuel).
I'll try to find some photos,but meanwhile here's a link to the "Russian Axe" thread on a Russian forum(axes shown there represent oh,maybe 150+/- years back from today):
https://rusknife.com/topic/17997-русскiй-топоръ/