There is not much difference between the two. The group I elements are highly reactive (more reactive than alkaline earth metals). Alkali is a noun meaning that the group 1 metals react with water to form strongly alkaline hydroxides.
Group II elements are called 'earth' metals as they show resistance to melting even at high temperatures. metals. Group II elements also form basic (alkaline) hydroxides. Hence, group II elements are called Alkaline Earth metals. Alkaline is used as an adjective here to describe the 'earth metals'.