Touch is a versatile sense. Your whole body can feel touch, and we can feel touch in multiple ways. I would say that your sense of touch is almost as versatile as smell in the emotions that it can convey.
The official sciency word for senses felt by the body is somatosensation. Somatosensation can be divided into mechanosensation (sense of contacting materials), thermosensation (sense of temperature), and nociception (sense of pain). We’ll focus specifically on mechanosensation.
Mechanosensation is what people usually think of when we think of sense of touch. Mechanoreceptors are cells specially built to detect mechanical properties. There are four main mechanoreceptors that detect data on the skin: Merkel cells (texture), Meissner corpuscles (motion), Pacini corpuscles (vibration), Ruffini corpuscles (stretch). When data is detected by these mechanoreceptors, signals are sent from the receptors to the brain through the spinal cord.
Piezo receptors are little channels on cells that open due to mechanical changes. When the piezo channel is moved in some particular way, ions flow into the cell. These ions signal to the cell that a change has been made. Mechanoreceptors tend to be unique arrangements in cells with piezo receptors, causing them to feel the certain stimuli we feel.