Ira Condit – in his famous 1955 monograph (Fig varieties; 4.2 MB, 247 pages), discusses two figs named Stanford: one on page 338 (Caprifig) and the other on page 351 (Smyna).
In c. 2008 the USDA fruit tree repository near Davis CA performed a year-long study of 126 fig tree accessions at their site. The Observation data shows
DFIC 92 “Stanford” is a Smyrna, and
DFIC 134 “Stanford” is a Caprifig.
Some sellers of caprifigs seem to have these accession numbers reversed.
Here is a photo of an immature fruit from the Caprifig, showing stamens forming near the eye. The background grid is 1".