Salesforce.com is a CRM system which has built in OOB functionalities to automate your Sales, Marketing, Services etc. We call this as SaaS (Software-as-a Service).

Force.com is a Platform-as-a-Service (PaaS) offering from the same company that allows you to build your own applications and/or customize the standard applications.

Salesforce.com also offers Force.com which as Platform-as-a-Service (PaaS) framework using which you can:

a) Customize and extend the core functionality offered by Salesforce
b) Create new applications and/or products

In layman language bellow is the difference between the two-

Force.com = iPhone OS.  The environment that can build and run apps.
Salesforce.com = The iPhone “app” that stores contacts, makes phone calls, + all the other standard functions of a phone.

Salesforce.com runs on the Force.com platform, much like the iPhone dialer runs on the iPhone OS.

If we dig a little more in details, the difference would go as below-

When you sign up for Salesforce.com‘s “sales cloud” – you get the CRM functionality that’s pre-built by Salesforce. You can use Force.com(and other tools) to customize your CRM or build new applications that are housed within your salesforce instance (organization).

Force.com includes the following major building blocks for building your applications:

a) Apex – Java like programming language for building your application logic(Controller)
b) Visualforce – for building application user interfaces(View)
c) Custom Objects – for storing your data(Model)

Apart from the above, the platform also includes other shared framework components that you can leverage – such as scheduling engine, email service, public facing websites etc etc.

Interestingly anecdotal references state that most of Salesforce.com is NOT built using Force.com – except for may be some pieces.