Well it used to have both elements and weapon types. Its hard to say whats gonna happen once its released after the rework.

Generally the weapon types work(ed) in a way where certain types could attack through multiple lines, while other could not, but would confer a status buff to the unit in front of them.

Not sure if you ever played the game and know how the battle system works, but a quick rundown.

Enemies are on the right, you units are on the left.
Your units are arranged in 3 rows. How you place them in those rows depends solely on you. Only girls in the front row can attack (exception is ranged girls who can attack from second row as well). You can either auto or manually rotate the rows, usually either when the girls get damaged, or you are saving up for a big combo and want to unleash it at a certain time.
Each girls builds her own Combo meter, and once full she uses her skill which can be a anything from a Single to mass AoE attack.
With the exception of Ranged girls, all other girls in the second row use buffs on the characters in the front row.
Those buffs work always only on the character that stands directly in front of them.

Thats pretty much what I remember how it used to be. The game is down over a Year by now, and my memories are getting really hazy.
How the elements work, I dont remember anymore, but its similar system like in FKG, where certain types have damage bonuses against others.
I believe there was an Elemental wheel pop up in the game, that you could always look at and it would show you which color is strong against which.

Also - but this is a super long shot - I remember someone posted a picture with ALL the weapon type explanations and the row system here (I think it was here and not in Nutaku forum).
But considering how long its been, its gonna be buried somewhere deep in this thread.
I am sure you`ll recognize it should you stumble upon it (in which case please repost again) in case you went on a search.

Anyway thats pretty much all I can remember. As I said the game has been down for so long most of the memories of the mechanics I still posses are rather vague. And they sure are taking their damn sweet time with the launch. Was promised to be this year and looking at its, I wonder WHEN NEXT YEAR its gonna be...