The US navy still has a good number of medium to heavy conventional propulsion cruisers, the Ticonderoga class and some nuclear powered ones, like the Virginia class.
The problem is that ships originally were classed by their displacement and, until 1950/60, is was pretty easy to classify ships, while now there are destroyers and frigates with more than 7000 tons of displacement, what by the older standards, puts them on par with most cruisers.
Also, the reduction of gun calibre to the almost universal dual function 127 mm, and the widespread of guided missiles, complexes even more naval typology. In fact , trying to compare ( and establish differences) between a modern Arleigh Burke destroyer and a modern cruiser can be painful.
The battlecruiser definition is even harder to conceptualise. The original term for them was "great heavy light cruiser", and that was how Lord Fisher, the father of the HMS Dreadnought, ordered them for the Royal Navy. Eventually someone started to think that "great heavy light cruiser" was a vague concept and classified the ships as battlecruisers, vessels capable of emulate the firepower of conventional dreadnoughts but still maintained the speed of cruisers.
Even so the designation battlecruiser always produced a fair amount of equivoques. For example, the battlecruiser HMS Hood , built between 1916 and 1919, with a displacement that could oscillate between 41 125 and 46680 tons; was bigger and heavier armoured than any contemporary dreadnought built until then, and by 1940 it still had a displacement similar to the North Carolina battleship class. By the displacement criteria alone, the Hood was, by his own right, a battleship, and the Kriegsmarine had no problems in classifying it as panzerschiffe (battleship or armoured vessel).The royal navy only categorized it as a battlecruiser simply because the Hood had a extremely high speed ( 31 .9 knots) and used torpedo tubes.
At the same time the HMS Renown and HMS Repulse also had firepower and displacements that matched the ones of Arkansas, New York, Nevada battleship and british Queen Mary dreadnoughts, but were universally classified as battlecruisers, while the pocket dreadnoughts of the Deutschland class , later known as the Lutzow class, ended up being considered heavy cruisers despite the fact that they were ordered as panzerschiffes and looked light when compared with the german Prinz Eugen heavy cruiser, and sort of puny if compared with the Scharnhorst and Gneisenau battle cruisers
To fire the furnace even more, the soviet nuclear powered Kirov cruiser was considered a battlecruiser by many western navies trough the eighties and even nineties, even when it had almost three and a half times more displacement than most occidental heavy cruisers ( and by comparison with them looked more like a battleship than anything else). But for the soviets it was always seen simply as a guided missile heavy cruiser.
It is all on the eyes of the beholder.