Are sensory mechanoreceptors and mechanical nociceptors the same type of neurons or are they different?
Short answer
Nociceptors are different from mechanoreceptors.
Background
Mechanoreceptors in the skin have specialized dendritic regions that facilitate their specific role in sensing different types of mechanical force, e.g., pressure receptors (Merkel’s disks) versus vibration receptors (Pacinian corpuscles and Meissner's corpuscles). See Fig. 1 for schematic representations of these types of receptors (Iheanacho et al). By contrast, pain receptors (or nociceptors) do not have specialized dendritic regions and consist of free nerve endings that respond to harmful mechanical forces (Purves et al., 2001).

Fig. 1. Skin receptors. source: Teach Me Phsyiology
References
- Iheanacho et al., Mechanoreceptors. In: StatPearls. Treasure Island (FL): StatPearls Publishing (2020)
- Purves et al., eds. In: Neuroscience 2nd ed. Sunderland (MA): Sinauer Associates; 2001. Nociceptors