If your second hand laptop only has an HDD (Hard Disk Drive), then, yes, the difference in performance between an HDD and an SSD (Solid State Drive) is like night and day.
M.2 is just a form factor. Do note that there are generally two interfaces used in an M.2 slot - a SATA-based M.2, or a PCIe-based (NVMe) M.2.
The SATA-based M.2 has a bandwidth similar to an SSD plugged into a regular SATA port (for SATA3.0, that's only about 0.6GBps), but, a PCIe-based M.2 has significantly more bandwidth (for PCIe3.0 x4, that's ~3.9GBps).
So, if your laptop already has a regular 2.5" SSD interfacing with the laptop motherboard via SATA connecction (not in an M.2 form factor), then, plugging a SATA-based M.2 SSD would generally have...