Disposable diapers are made from plastic for the water proof cover which is made from oil.
Yes even modern disposable diapers even though they're cloth like they're not actual cloth. Underneath the cloth cover is a plastic out shell that holds in the wetness.
Although sometimes wetness can still seep through.
The same goes for Adult Disposable diapers. The cloth like ones have an plastic barrier underneath the cloth cover as well.
For the Adult and baby diapers to absorb the diaper companies use a chemical called SAP "Super Absorbent Polymer" This Sap increases in size "Swells Up" when it soaks in water or urine.