No, Foxtail Ferns and Asparagus Ferns are not the same plants though they are commonly mistaken for one another. The Foxtail and the Asparagus Ferns are not ferns but instead apart from the perennial evergreen family.
An easy way to tell them apart just from appearance is the growth pattern of their stems. Foxtail ferns do better in a standing pot due to their upright stems. Asparagus ferns do better in a hanging or high basket because of their limp and flowy foliage.