The biggest factor is their overall size. A Russian Karakurt class corvette (of which the OP ship is a member) displaces 860 tons, while a US Arleigh Burke class destroyer displaces over 11x as much weight at 9.700 tons. That combined with significantly lower wages in Russia pretty much accounts for the entire difference.

Additionally, the Burke's superstructure clearly has much more 'stuff' on it than a Karakurt does, so in addition to being much larger, a Arleigh Burke is going to be much more capable at various tasks.

US destroyer

I know the US calls them destroyers, but they are the size of a WWII light cruiser. The Atlanta class light cruisers displace 8.300 tons; they are actually lighter than a modern Arleigh Burke destroyer!

To start with, they aren't cruisers. This is a missile corvette, the closest equivalent in the US fleet would be a littoral combat ship. That may not look much better in terms of cost, but to generalize on displacement/capability corvette -> frigate -> destroyer -> cruiser. The Russian ship here featured 8x VLS capable of Calibur missiles and a ship borne Pantzir air defense system. By way of comparison my country is building a new class of frigate which will carry 8x Naval Strike Missiles, 24x Sea Ceptor missiles, 24x multirole VLS, 2x twin 324mm torpedo launchers, and a helicopter (some guns etc). Hopefully that gives an idea of how important it is to not randomly use terms like "cruiser" for any ship painted grey by certain media outlets.