In Deep Q Network (DQN), the Q network itself is the policy. You have one output for each possible action, and the the neural network estimates the Q value for each action in the current state. You act by selecting the action with the highest Q output. This doesn't work if the action space is continuous, e.g. motor torques for a robot.

You might think you can fix this by making the action an input to the Q network and keeping only one output; then you could find the action with the highest output. But due to the nonlinearity in the neural network, this is an intractable nonconvex optimization problem.

So instead, you train a neural network to output the action given the state. The algorithms are harder to understand, because Q learning is kind of like supervised learning but policy gradients really aren't. A lot of algorithms (A2C, DDPG, TRPO, etc.) still use one-output Q network (as described in the previous paragraph), but this is just a part of the learning algorithm * . Once training is done, you throw away this Q network. The learned behavior is entirely contained in the policy network. These methods are usually called policy gradient methods.

This article covers policy gradient methods only.

* it's possible to do "pure" policy gradients using only the empirical return, but the Q network helps reduce the variance of the gradient estimate and stabilize the learning.