Is a multi-layer perceptron exactly the same as a simple fully connected neural network?
Yes, a multilayer perceptron is just a collection of interleaved fully connected layers and non-linearities.
The usual non-linearity nowadays is ReLU, but in the past sigmoid and tanh non-linearities were also used.
In the book, the MLP is described this way:

An MLP is composed of one (passthrough) input layer, one or more layers of TLUs,
called hidden layers, and one final layer of TLUs called the output layer (see
Figure 10-7). The layers close to the input layer are usually called the lower layers, and the ones close to the outputs are usually called the upper layers. Every layer except the output layer includes a bias neuron and is fully connected to the next layer.

(&quot;TLU&quot; stands for threshold logic unit)