can someone help me out here?

Not much but as I see it a Spellsword uses magic to support his own melee combat while Battlemages support others and fight from a distance with their magic and use melee as a fallback. A problem is that Battlemage is defined differently in-lore and in-game. In-lore a Battlemage is pretty much any mage on the field of battle, lobbing fireballs at the opposing lines or a group of them helping an army march under a lake to attack a city, while in-game they're heavily armored melee-magic hybrids.

Spellsword is more defensive based, whereas battlemage is more aggressive.

A Battlemage tends to be more "tank" like, while a Spellsword is more nimble. In terms of weapons Spellswords obviously favor swords, while most Battlemages use more crude weapons like axes and maces. Battlemages are also more magic-orientated than Spellswords.

Spellsword-More nimble and athletic than the sorcerer, and better suited for spell-casting than the knight, their attacks are unpredictable. Students of combat and magic.

Battlemage Able to resolve most conflicts with either spell or sword. They are a deadly mix of scholar and soldier.

That's there in-game definition, hope it helps!

Also here's there stats

Spellsword
Specialization: Magic
Attributes: Intelligence, Willpower
Skills: Alchemy
Alteration
Conjuration
Destruction
Illusion
Mysticism
Restoration

Battlemage
Specialization: Magic
Attributes: Intelligence, Willpower
Skills: Alchemy
Alteration
Conjuration
Destruction
Illusion
Mysticism
Restoration