My girlfriend recently purchased a couple of new houseplants for our home. When she got them home, however, we realised that neither plant included a label to identify it. My best guess currently (based on essentially zero horticultural knowledge) is that they're both some form of Chinese Evergreen, but I'd be grateful for any help with identifing them, and, if possible, some simple advice for how best to care for them.
The second one is a Codiaeum, commonly known as croton - it needs some sun and prefers high humidity. Keep it away from heat sources, and water when the surface of the soil feels just about dry to the touch - when you do water, water well, and empty out any outer pot or tray after 30 minutes. Further growing advice here https://www.almanac.com/plant/croton#
I believe the first one is most likely Aglaonemia (chinese evergreen); this one shouldn't be placed where it gets direct sun, just medium to bright daylight. It also prefers higher humidity - watering instructions similar to those mentioned above. Further care info here https://www.houseplant411.com/houseplant/chinese-evergreen-how-to-grow-care-tips
If you have pets, both these plants are toxic if ingested, though Aglaoenemia is more so.
UPDATE: Now you've added a second photo, the first plant is actually Dieffenbachia, not Aglaonemia; it's what I was somewhat doubtful about when I first answered and I should have asked for a second photo at the time.
Dieffenbachia is not so fussy about humidity - otherwise, light requirements and watering instructions are the same as for Aglaonemia. Also the same warning about pets not being allowed to chew the leaves, further info here https://gardeningsolutions.ifas.ufl.edu/plants/houseplants/dieffenbachia.html