Most people always confuse Babylonians with Neo-Assyrians or vice versa but you can easily distinguish them by looking at their crown/cap and clothing. Assyrians have a spiky cap which looks almost like some little pyramide on their heads (right guy above and/or right one in pic no. 2) whereas the ones of Babylonian kings are simpler and usually miss those two ribbons behind the head. Also only Assyrians wore those clothes with scarf-border (pic above, the right one or everyone in the lower pics) and those wrist-watchlike flower-bracelets + their hairs ended on their shoulders with those hair…balls or whatever they are called - Babylonians rather had long, open hairs like Marduk above on the left.
Although those two peoples shared the same culture they became rather different throughout the first millenium BC. Few examples:
- Neo-Assyrians were very militaristic and always recorded things they did on their campaigns, including describtions of killings or destruction in general, Babylonians refused to do this (which is somehow problematic for archeologists since they have barely any infos about wars they fought) and concentraded on writing down what they did for their gods (= temples they built and how they decorated them etc. you know, the cultural things).
- If you know enough, you will be able to distinguish their art immediately. Neo-Assyrian art and its symbolism is rather influenced from Syria, Egypt and Anatolia and because of that a bit different from Babylonian art + they depicted different things (Assyria mainly god Assur in the winged disc with tree of life and genius or war centered topics).
- The main god of Assyrians was Assur, who was more or less a god of war who was rather distant and whose cult already had some traits of monotheism, whereas the main Babylonian god of that time was Marduk who was one of those gods people prayed at - the almost-monotheism wasn’t that evolved there either and Assur was more or less non-existent there.
To illustrate the problems between them I can give Sanherib (Sennaherib) as example who totally destroyed Babylon after a bunch of wars and problems with them and even redirected the main waterway into the city to drown the people and flood the whole metropolis. Although this was an extreme case (and Sanherib was killed later by his own sons) it shows that those two empires weren’t the same thing although you could consider them as some kind of brothers who either fight or like each other (and have the same parents of course).
By the way, the pic above shows a whole different case; there Salmanassar, the mighty king of Assyria, helped the Babylonian king when he was in trouble (he almost got overthrown). The relief was made after that to show those two being bros.