The Client is a Company. The Contact is a person who works for the company.
Here are a few scenarios that may help
ABC Law Firm (Company) has 25 Attorneys (Contacts) that work for them.
ACME Insurance (Company) has 5 Adjusters (Contacts) that work in the office. ACME is the company you will enter in the system one time. The 5 adjusters would be entered individually as contacts for that client.
For more information on adding and managing contacts, check out the video tutorial below