Hey Nick.
Great to hear your shaving experience with the Headblade is getting better. Most Headbladers on this site had a mirrored experience that you had but after patience and practice, they now swear by it.
The HB Classic (and Sport I assume) comes with 2 adaptors that fit the Atra style cartridges which also happen to be the same of the HB brand doubles and triples. There is also a 3rd adaptor that comes with it that will fit the Sensor cartridges. The color isnt important as my adaptor that fits the HB doubles and Atras is Black and my Sensor adaptor is yellow.
Nick some HB devices may not include these adaptors. I purchased the 20 blade refill HB double kit which came with these 3 adaptors. The HB itself only comes with the HB/Atra adaptor.
Personally, I prefer the Sensor cartridges(double blades). The problem with Triples IMHO is that the razor gunks up too quickly and therefore doesnt provide as smooth a shave. Again this doesnt apply for everyone as there are quite a few SBG's who use the Triples.