The botanical name for serrano pepper plant is Capsicum annuum var. annum (Longum Group) 'Serrano'  

As the part of the pepper plant that we normally eat is a seed-bearing structure, a serrano pepper is technically a fruit!  Even more technically, it is a berry.

Berry: An indehiscent (does not split open) fruit derived from a superior ovary with a thin exocarp (skin) and fleshy mesocarp and endocarp, e.g., grape (Vitis, Vitaceae), tomatoes & eggplant (Solanum, Solanaceae), bell peppers & chili pepper (Capsicum, Solanaceae), date (Phoenix, Arecaceae), avocado (Persea, Lauraceae), persimmon (Diospyros, Ebenaceae), guava (Psidium, Myrtaceae).

(definition from Northern Ontario Plant Database)

Courtesy of the NYBG Plant Information Service