What are the differences between MLP and DNN?
You explained it already quite well. An MLP is a type of neural network, the same way CNNs, RNNs, and other types exist. DNN is an umbrella term for all types of neural networks.
The reason some literature may be using these terms interchangeably is likely due to the fact that MLPs are some of the oldest forms of neural networks and therefore, at the time the literature was written, MLPs and DNNs were ubiquitous.