I think the jalapeno is purely Mexican. The Spanish peppers you mention are likely Padrón peppers rather than Jalapeno, they are from Galicia, northwest Spain bordering Portugal. In Galicia, they are picked young (about 1" long) when about 1 in 12 is hot. As they progress, they all turn hot. They are of the same variety as Jalapenos ( Capsicum annuum) and are similar in appearance. Apparently the Bird’s eye is also of that variety.
I have a (very) small greenhouse and have been growing Padróns for about 5 years, I started with seeds I bought from Maine, but would like to find a legal way to get seeds from my family’s farm in Galicia.