“Contemporary” typically means of the moment or current, the design of right now. “Modern” refers to a specific design style from the early to mid 20th century that broke with the traditional styles of the days before the Industrial Revolution.
When I think of modern kitchen designs, I think of frameless cabinets, sleek and simple hardware, strong horizontal lines and a lack of ornamentation, with the natural beauty of the materials shining through.
Looking at the Houzz page on Contemporary kitchens, I’m biased to their definition of “modern”.
Back to the Modern Kitchen look and feel:
Flat panel door style (aka slab-door)
Full overlay door, ie the door overlays the cabinet box.
Lack of ornamentation. ie no patterned tile shapes or multiple materials with textures. So sleek hardware, full height glass splashback. No patterns or veining on coutertops.
Emphasis on horizontal lines.
The picture below is also from Houzz. Long clean lines.
– but on the detail, I want the hob elements on the island, not the sink. It’s more social to cook around the hob and putting the sink on the back wall means dirty dishes and dishes that are drying are more out of sight.