People call it DDR because that's what everyone knows about and what it looks like. Don't get your panties in a bunch.
But the only similarities the games have with each other is that they both have notes scrolling to a receptor and you have to hit the corresponding button on the dance pad with correct timing, literally everything else is different. It's fine if they say it's like DDR but when they call it DDR with the obvious differences shown to them, I just will not have it.
I dislike Pump it up. Ddr is more fun and more arcades have ddr imo
I like both, and I'm at the same skill for both games, slightly more with DDR. Only thing I hate about DDR is how they include a bunch of steps that make you do spins or just turn around completely making it so you have to hit two consecutive steps with one foot.
Pump looks stupid anyways. Looks like Stepmania screenshots, so I'm going to have to say that Beat is the best mode aside from Dance.
You obviously have not seen what Pump can do that Dance can't.