Is athletes foot the same thing as a yeast infection?

Not exactly: Both athlete's foot and yeast infections are cause by organisms in the fungus family. Athletes foot can be caused by several different types of fungus as well as yeast. Many of the same medications which can be used to treat yeast infections will also benefit athlete's foot. A related condition, jock itch, can also be commonly caused by yeast as well as traditional fungi.

Sort of: Athlete's foot is a type of fungal infection specific to the foot.

Yes: Athlete's foot is a fungal infection (yeast) of the skin of the foot, brought on because of the warm moist environment created by the sock and shoe.

Not quite: Both conditions are due to a fungal infection, just in different areas of the body. Both are also treated with anti-fungal creams (and pills for the yeast infection.).

Nomenclature: Strictly speaking, yeast and molds fall under the broader category of fungi (which also include mushrooms). Athletes foot is a skin infection by a dermatophyte called trichophyton rubrum, these are hyphal fungi that only infects top layers of skin. The yeast infection we generally refer to is caused by candida albicans, a budding yeast, thrives in moist areas such as skin folds and mucosal areas.

Yes: Athletes foot is a yeast infection on the foot.

Treatments differ: The reason it is important to distinguish yeast vs dermatophytes is how we treat them. Some antifungals target only dermatophytes, some are better against yeast. Over the counter Lamisil (terbinafine) is more effective against dermatophytes (athlete's foot) and lotrimin better against yeast (jock itch). That said, the above 2 examples can have overlapping infections of both yeast and dermatophytes.