What is pediatric asthma compared to adult asthma?

More likely allergic. Allergy is present in 90% of children with asthma but only 50% of adults with asthma.
Babies are different. At least 50% of babies will wheeze at some point in their first year of life, because the airways of babies are still developing. The babies don't all have asthma. Until about the age of 6, children are more likely than adults to have transient wheezing that isn't really asthma. By age 10, kids are similar to adults. Here's a link: www.Ncbi.Nlm.Nih.Gov/pubmed/11803801.