Lombardo Loventhal

You can describe a recurrent neural network (RNN) or a long short-term memory (LSTM), depending on the context, at different levels of abstraction. For example, you could say that an RNN is any neural network that contains one or more recurrent (or cyclic) connections. Or you could say that layer $l$ of neural network $N$ is a recurrent layer, given that it contains units (or neurons) with recurrent connections, but $N$ may not contain only recurrent layers (for example, it may also be composed of feedforward layers, i.e. layers with units that contain only feedforward connections).

In any case, a recurrent neural network is almost always described as a neural network (NN) and not as a layer (this should also be obvious from the name).

On the other hand, depending on the context, the term "LSTM" alone can refer to an

People may also refer to neural networks with LSTM units as LSTMs (plural version of LSTM).

An LSTM unit is a recurrent unit, that is, a unit (or neuron) that contains cyclic connections, so an LSTM neural network is a recurrent neural network (RNN).

The main difference between an LSTM unit and a standard RNN unit is that the LSTM unit is more sophisticated. More precisely, it is composed of the so-called gates that supposedly regulate better the flow of information through the unit.

Here's a typical representation (or diagram) of an LSTM (more precisely, an LSTM with a so-called peephole connection).

This can actually represent both an LSTM unit (and, in that case, the variables are scalars) or an LSTM layer (and, in that case, the variables are vectors or matrices).

You can see from this diagram that an LSTM unit (or layer) is composed of gates, denoted by

and recurrent connections (e.g. the connection from the cell into the forget gate and vice-versa).

It's also composed of a cell, which is the only thing that a neuron of a "vanilla" RNN contains.

To understand the details (i.e. the purpose of all these components, such as the gates), you could read the paper that originally proposed the LSTM by S. Hochreiter and J. Schmidhuber. However, there may be other more accessible and understandable papers, articles or video lessons on the topic, which you can find on the web.

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