When is something a Deep Neural Network (DNN) and not NN? When would a neural network be defined as a Deep Neural Network (DNN) and not a NN?

A DNN as I understand them are neural networks with many layers, and simple neural networks usually have fewer layer... but what a many and a few in numbers? or is there some other definition?

What are networks trained used Tensorflow, Caffee as such? I haven't (as far I know) seen anybody manually design a network with many many layers. 
They seem to promote their tools for creating DNN, but is it actually DNN if you only make a network with two layers?
You are right. Mainly any network with more than two layers between the input and output is considered a deep neural network. Libraries like tensorflow provide efficient architecture for deep learning applications such as image recognition, or language modelling using Convolutional neural networks and Recurrent neural networks. Another thing to keep in mind, is the depth of the network also has to do with the number of units being used in the layer. Mainly, as your non-linear hypotheses get complex you will need deep neural networks.