There are a few differences to be aware of between these Droplet types. To answer your first question: The main difference between High CPU and Standard Droplets from a CPU perspective is that High-CPU Droplets have dedicated hyper-threads with best-in-class underlying physical CPUs and Standard Droplets have shared vCPUs from more Standard performing underlying physical CPUs.
Typically what we see with customer workloads running MySQL is that they aren't bound by CPU but typically need more RAM (for caching database data and indexes) and local SSD (for decreasing network latency).
In this case: you may be better suited running your MySQL database on a "High Memory" Droplet. With the $120 High Memory Droplet, you'll get the same amount of RAM as the $160 Standard Droplet but save $40 and have an ample amount of SSD unlike the High CPU Droplets.