When drilling pilot holes in wood for wood screws with cut threads, it is important to take your time. Each hole will need to be drilled three times!
The first hole will be for the threaded portion of the screw. Since the threads are cut into the nail, the hole must be smaller than the size of the screw. Templates exist that offer guidance for selecting pilot hole sizes.
https://www.boltdepot.com/fastener-information/Wood-Screws/Wood-Screw-Pilot-Hole-Size.aspx
After you drill the pilot hole for the threaded portion, you will need to drill another hole for the shank.
Lastly, you will need to drill the third and last hole to countersink the head. It is a good idea to countersink the head at least to make it flush. As the wood wears away over the years, this will keep the screw head just below the surface. If you are going to walk over this fastener, it won't dig into your foot, and if you are going to stand next to this fastener, it won't cut your leg or rip your clothing.
The important thing to remember is that you should drill the hole three times, once for the threads, again for the shank, and lastly for the head. Then the fastener will be able to hold everything together as best as it can while being out of the way.
