Both auxins and gibberellins are plant hormones that function to promote plant growth through cell elongation. Auxins, in particular, respond to the influences of light availability and gravity, and also promote the differentiation of vascular tissue. Gibberellins are more responsible for growing shoots and promoting cell division in addition to cell elongation.
Auxins and gibberellins are both types of plant growth hormones but they differ in substantial ways. Auxins are classified purely by their function, and the only biologically active natural form is indole acetic acid. Auxins also inhibit budding off the side of stems and branches, instead promoting budding at the tip of the growth. They play a critical role in flowering and fruiting and can actually stimulate fruiting in unfertilized flowers. Synthetic auxins are often used as herbicides.
Gibberellins, in contrast, are classified by function and chemical makeup, and around 125 different hormones fall into this category. They share a function of promoting fruit and flower development with auxins, and also promote seed germination. Like auxins, they can promote the development of seedless fruit development. They also act as sex hormones, promoting maleness in flowers with only one sex. Their presence delays the death and shedding of leaves.