What is exactly meant by neural network that can take different types of input?
In short, can I create neural network that takes different types of
  input individually or do I use different neural networks for each of
  them and then group their outputs?


Yes, you can. Check the Functional API of Keras, on how to define multi input/output networks. Then you can create different models for the processing of each input and fuse them together into a single multi-input model using the keras.models.Model() class.

In the following example, you can see that the main_input is processed differently than the aux_input and both are thereafter merged together to be propagated through the rest of the layers of the network.