Yes they’re the same species - they’re all Syrian hamsters. I think it’s generally the long haired Syrians they call “teddy bear” hamsters.
Syrians can come with various types of coats. Short hair, long hair, satin coat (a particularly shiny short hair) and Rex (wavy hair). And a variety of different colours, from breeding over the decades. Originally they were all “golden “ hamsters. Below is a list of all the variations of fur type and colour within the Syrian hamster species.
This article is by a bona fide breeder and explains it well. They also explain the dangers of some of the marketing terms used to sell Syrians by giving them different names like teddy bear , black bear and so on. I think your friend would find it very interesting and useful.
Syrian Hamster Varieties - Harvey Hams