Most adult mattresses are perfectly suitable and safe for children. Whether a mattress is designed for kids or adults, it must pass the same material and safety inspections in order to be sold to the public.
That said, mattresses made with kids in mind are typically a better fit for children. Many of these models come equipped with features not found on adult mattresses, such as waterproof barriers to protect the internal components from damage during bedwetting episodes. Some of the leading mattresses for kids have reversible designs with a firmer surface to promote healthy development for your child, and a softer side to accommodate their evolving comfort preferences as they age.
Sizing is another consideration. Queen, king, and California king mattresses are probably overkill for a child, as these sizes are geared toward couples and offer a lot of surface area. A twin, twin XL, or full size should provide adequate space for a child of any age. This is particularly true for kids who sleep in bunk beds, as most bunk models are only compatible with these three smaller sizes.