These a cancers of white blood cells. Basically, there's acute lymphoblastic leukaemia (ALL - this is pronounced "AY-ELL-ELL", not "all") and acute myeloid leukaemia (AML). ALL is the biggie in paeds, and there's probably a load more but I'd rather learn about the common ones, to be honest. AML is the one you need to know about in adults.
Just like leukaemia, there's two basic types based around a bloke called Hodgkin who I assume was pretty damn clever. There is Hodgkin's lymphoma and non-Hodgkin's lymphoma. Presumably, he was pretty badass if he got a whole set of cancers named after him. The former is more common in adolescence, the latter in childhood. The difference is, well, some clever histological magic.