There is much confusion about the use of the terms "pressed" and "processed" and it is helpful to understand the difference.

Many carrier oils and essential oils are used in the manufacture of our body care products and soaps.  These have, in many instances, been pressed from the flesh, seeds, leaves or roots of plants without the use of high heat.  These oils are referred to as cold pressed as they are truly pressed.

When making soap, however, we use different "processes" to make our product.  Cold processed is the most popular, which is processing the soap without use of high heat.  We do not press it.
Hot process is another method used that does involve high heat, but it is a process.  We still do not press it.
There are other processes you may come across in your research but they are still processes.  The only time a soap is pressed is in a commercial facility where it may be moulded and needs to be pressed into the mould.