A perceptron is always feedforward, that is, all the arrows are going in the
direction of the output. Neural networks in general might have loops, and if
so, are often called recurrent networks. A recurrent network is much harder
to train than a feedforward network.
In addition, it is assumed that in a perceptron, all the arrows are going from
layer $i$ to layer $i+1$, and it is also usual (to start with having) that all
the arcs from layer $i$ to $i+1$ are present.
Finally, having multiple layers means more than two layers, that is, you have
hidden layers. A perceptron is a network with two layers, one input and one
output. A multilayered network means that you have at least one hidden layer
(we call all the layers between the input and output layers hidden).