Both actuaries and statisticians have similar skills sets, such as computer knowledge, mathematical knowledge, and the use of statistical techniques. Where they differ is their employment settings, and the scope of their work.
Actuaries work specifically within the insurance industry, and handle data related to risk, providing companies with statistical probabilities of future occurrences. They focus on the financial losses that are associated with accidents, illnesses and natural disasters, and help insurance companies assign what coverage and premiums the client should be charged.
Statisticians (sometimes called data scientists) can work in a variety of settings, with multiple types of data. They are employed in banks, government agencies, consulting firms, technology firms, health-care organizations.. anywhere that collects and handles large amounts of data. They use statistical techniques to extract, analyze and summarize, turning complicated data sets into usable information. This information is then given to management, which will in turn use it to make informed decisions and policies.
A neurologist is a medical doctor who specializes in treating diseases that affect the human nervous system.