onmouseenter / onmouseleave event of a DOM element will be triggered only when the mouse cursor enters / leaves the element:
Demo of MouseEnter & MouseLeave event
onmouseover / onmouseout event of a DOM element will be triggered not only when the mouse cursor enters / leaves the element, but also when the mouse cursor enters / leaves sub-elements of the element.
Demo of MouseOver & MouseOut event
|||Mouse Events - QuirksMode|