Stenaelurillus jocquei was first described by Dmitri Logunov and Galina Azarkina in 2018.[1] It was placed in the genus Stenaelurillus, first raised by Eugène Simon in 1886. The genus name relates to the genus name Aelurillus, which itself derives from the Greek word for cat, with the addition of a Greek stem meaning narrow. It was placed in the subtribe Aelurillina in the tribe Aelurillini by Wayne Maddison in 2015, who listed the tribe in the clade Saltafresia. Two years later, in 2017, it was grouped with nine other genera of jumping spiders under the name Aelurillines. The species is named after Rudy Jocqué, the collector of the type series.
The spider is medium-sized and appears in two forms, which have identical copulatory organs but different colouration. These are termed the light form and dark form.
The male of the light form has a brown carapace that measures 2.7 mm (0.11 in) in length and 1.9 mm (0.075 in) in width. It is covered in dark brown scales and has two wide stripes made of white scales, along with edging also of white scales. The abdomen is brown, 2.4 mm (0.094 in) long and 1.75 mm (0.069 in) wide, and has a pattern consisting of three white spots and three white stripes. The eye field is dark brown and is decorated with long brown iridescent hairs. The chelicerae is yellow with brown hairs and the clypeus is yellowish brown with yellow hairs, also iridescent. The spinnerets are brown, the legs are brown and yellow and the pedipalps are yellow. The palpal bulb is shaped like a bulge and has distinctive appendages. The embolus is long, spiralled and ribbon-like.
The light form female is similar to the male in shape but overall slightly larger. The carapace the same length but 2.2 mm (0.087 in) wide and the abdomen has a length of between 3.0 and 3.5 in (76 and 89 mm) and width of between 2.25 and 2.8 mm (0.089 and 0.110 in). The colouring is similar to the male but lighter, and the iridescent hairs are lacking. The spinnerets and legs are all yellow, while the pedipalps are yellow with brown bristles. The epigyne is flat and has a deep narrow pocket. The copulatory openings are large and has a heavily sclerotized rim. It has short and wide insemination ducts and large round spermathecae.
The dark form differs in that it has a slightly shorter carapace 2.6 mm (0.10 in) long and has a darker abdomen that is 2.5 mm (0.098 in) long and 1.7 mm (0.067 in) wide. The chelicerae and clypeus are brown and covered with very dark brown hairs. The pedipalps and spinnerets are also darker brown and the legs darker too. The spider is very similar to Stenaelurillus hirsutus, although it has two rather than three stripes. The longer spiralling embolus is a distinguishing feature of the male, while the way that the pocket in the epigyne of the female sits between the copulatory openings and the round, rather than elongated spermathecae, differentiate the female.