Can we make two separate models vs one for classification?
That doesn't make much sense, no. If you provide all the data to both models, they should perform exactly the same. If you only provide positive data to each model, you're making two incomplete models that (supposedly) won't learn as well as using all the available data. Making multiple models to a single response variable can make sense, but not when the response is binary.

If you happen to also have unlabeled then it's a different thing, because you can use techniques such as the two-view models. But in practice, it's often more useful to spend resources labeling data than developing a semi-supervised model.