Both, Business Analyst and Functional Analyst’s roles are different, even though they may work in the same company. A Business Analyst is a professional who is on the management side of things, who takes of the businesses, collects data, analyzes it, and extracts valuable insights from it, to empower business decisions, to help grow the business effectively, by offering key data-driven solutions.
Now, Functional Analyst's role is to oversee the implementation of these solutions which these Business Analysts have suggested. Functional Analysts select which suggestion or the solution to go with, and based on their expertise in their own field, specific technology, domain, or industry they will work towards its implementation. Since Functional Analysts have the technical knowledge of software, they are capable to perform end-to-end tasks, from installation to troubleshooting errors within software.
If you wish to become a Business Analyst, then check out the Business Analyst course from Intellipaat. Also, have a look at the following video on How to become Business Analyst with No Experience.