They were different. VERY different. One was a waterbender. And the other an earthbender.
Out of all the members in the Gaang it was Katara and Toph who fought the most. Not even Zuko's personality could beat their fueds. The girls weren't alike in how you would think whatsoever. They fought constantly and argued aggressively.
It was weird though. The girls were really polar opposites.
Katara was always graceful. She was loving. She was a dark beauty. Elegant ,though not in a royal way, but still classy. She was the moon. Everywhere she went she glowed in the darkness with a peaceful shine. Eyes so blue, one can instantly see the flowing element in the twinkling orbs. Katara represented her nation greatly. She was fluid and lovely just as she was demanding. She didn't want perfection but still she wanted things in place. Katara was sweet. Delicate and feisty. She never takes anyone's nonsense. Always giving her all.
Toph was the opposite. Toph was a strange one. A little bigger of a mystery than Katara. Where katara was soft, Toph came out rough. She was solid. Her bending always perfect and her statements always straightforward. She didn't prefer that delicate flowery type of beauty . The girl didn't care about things based on appearances. Though the few times she permits it, one would obviously tell that such a lovely face ,flawless skin and silky long pitch black hair must be of noble blood. Toph can be pretty brutal. She hits you with facts as hard she can hit you with her earthbending. Unlike katara, she likes it when people hear her rather then see her. She tends to hide her filmed eyes by either turning her body or head, or just plainly looking down letting her hair shield her visionless eyes from everyone. She is hardheaded, she is compacted as she is loose. Toph is graceful, but also rough. She never takes anyone's bull just like she'll never give away anything halfass.
The girls are polar opposites. Very different. They fight constantly, whether it's from being filthy or clean, to being irresponsible or too bossy.
As the girls are unalike , they also carry a lot of similarities. If anyother member is ever troubled , they would both do their best to help. Both are wise girls. Prodigies of their own respects. And intelligent, never playing one's fool. The girls are stubborn. But even their differences are similar. Where one would instruct you to take a breather and relax from all your stress , another would tell you to focus and rejoice with the fact you're still alive.
They fight. They argue. They are both negative and positive. Different in NUMEROUS ways. But they are like sisters. They aren't like Azula, Mai and Tylee . Katara and toph's relationship is exactly like the mix you get when putting together water with earth, (MUDDY). It's a dark friendship meaning you can't exactly see through it. It's fluid, able to change as well as it is thick and full. The girls are best friends. And with their fights and violent banters they are really close, they love each other. Not one or the other wishing to change their sister whatsoever in the end.
One might even say that they're fiery discussions and fights are how they cope and stay sane with all the stress they have too experience on a daily bases.