Rims are designed, built and drilled for a specific number of spokes. The engineering that goes into the rim thickness, profile, and use case depends in part on the number of spokes.
I've seen a pair of 96 spoke wheels (which was build for a lowrider and was mostly for show)
I've owned a 48 spoke rear wheel on a touring/racing tandem- two 90+ kilogram riders need extra load support
I ride a 36 spoke rear on my road bike, because I value reliability.
On the other end, lower spoke count wheels exist but they tend to be built on special spokes.
16 spoke front wheels are common on road-racing bikes.
Spinergy wheels had 8 carbon "flats" functioning as spokes.
Some fancy wheels have 4, 3, or even 2 spokes, but they're a lot more complex than the conventional metal wire spokes we're used to.
There are disk wheels made out of one piece of carbon fibre (this is not wheels with covers over normal spokes) These might be construed as one single spoke, as wide as the wheel is around. But that's getting extreme and expensive.
Why? The lighter your bike, the faster it is. Removing spokes saves weight (but the remaining spokes have more work to do, sometimes requiring to be thicker negating weight savings.)
The fewer spokes on your wheels, the less disturbed the airflow gets as you ride. 32 spokes would cut the air twice as often as a 16 spoke front wheel.
Thinner spokes disturb the air less, and bladed/aerofoil shaped spokes are even better than round ones.
So the wheel you saw was probably a low spoke count racing wheel. Sometime Cafe-bikes are low spoke count for appearance.
Downsides of fewer spokes means that there is less load carrying capacity, one spoke breaking can untrue your wheel suddenly to the point it won't spin (happened to me!)
And the spokes cost a lot more to replace. I was paying $15 for a bladed spoke when a normal quality DTSwiss round spoke was about $2.
As for your bike, you can fit any wheel that matches your axle specifications and brake requirements, and fits in your bike without rubbing. Do check that the wheels are rated to carry your weight plus your bike's weight plus anything you might carry in a backpack, plus some tolerance.
Note that you don't have to have matching wheels - for a year I rode a 12 spoke rear wheel and a 32 spoke front wheel, it just looked odd but worked fine.