Still seems to be a lot of subjectivity in this. So would it be safe to assume that battlemages are normally in heavy armor while spell swords are in cloth? Cloth has more caster stats on them while you have to use enchants to get good caster stats on heavy armor.
Thanks to significant inconsistencies in the primary skills for both classes over the course of the prior four games, Bethesda has muddied the waters regarding the distinctions between these two classes more than a pack of Mammoths tap dancing in a small pond. That being said, based on
The Official Game Guide to Elder Scrolls V: Skyrim these are the suggested builds for Spellsword and Battlemage:
Spellsword
Health 40% /
Magicka 30% /
Stamina 30%
Primary Skills: One-Handed, Destruction
Secondary Skills: Light Armor, Illusion
Battlemage
Magicka 60% /
Health 40%
Primary Skills: Destruction, Restoration
Secondary Skills: Illusion, Heavy Armor
There's more detail in the Guide but the gist of it seems to be that Spellswords use Light Armor and rely more on One-Handed weapons but also use Destruction magic while Battlemages use Heavy Armor and Destruction magic. The former are warrior mages while the latter are mage tanks.