Elementals are stronger, faster, with better senses and more connected to nature than ordinary humans, they are still human, but enhanced. They have a strong connection to nature and its creatures, so they may be able to create some sort of bond with a specific creature, and their gifts are totally natural and have almost total control over the element they are born into. But they are limited to using such abilities, using other spells can be fatal to an elemental and break their connection with nature. If the elemental doesn’t die the first time they try to use spells, they would probably lose their gifts and become extremely ill, and may in fact die later. The only magical exception for elementals are runes, which can be used without spells or the user actually using magic.
Wizards are born with magic, but unlike elementals, they are only human, unenhanced but can use spells at will, but having control over one or more elements can be complicated, very complicated. It would require training and a lot of study, but it can be dangerous, the elements are not to let themselves be dominated easily by someone not elemental.