Smaller BMX bikes (assuming you are looking at 20 inch wheels only) have smaller handlebars, shorter cranks, sometimes shorter frames (depending on what it is) and angles can vary. Kids bikes are usually cheaper and have cheaper parts.
According to The BMX DudeDUDE
BMX Bike Size Chart By Height & Wheel Size
Wheel size Rider height Top tube length 12″ 2’4″ to 3′ 12″ – 13″ 14″ 2’8″ to 3’6″ 14″ – 14.5″ 16″ 3’2″ to 4′ 16″ – 16.5″ 18″ 3’10” to 4’8″ 18″ – 18.5″ 20″ 4’8″ to 5’2″ 18.5″ – 20″ 20″ 5′ to 5’4″ 20″ – 20.25″ 20″ 5’2″ to 5’6″ 20.25″ – 20.5″ 20″ 5’4″ to 5’8″ 20.5″ – 20.75″ 20″ 5’6″ to 6′ 20.75″ – 21″ 20″ 5’8″ to 6’2″ 21″ – 21.25″ 20″ 6’+ 21.25″+
In 20" wheels frames range from 18.5" to 21.25". As an example (not a recommendation), an online store that has filters for BMX bike top tube sizes between 18.52" and 21.95" when 20" wheel is selected.
Go ahead and get a bike that you like and does what you want.
Then, see if the kids can ride it. If they can't ride your bike, find something inexpensive for them to ride (maybe used). You don't really want them to ride your bike anyway :)