First, using Server 2003 for this small business is a mistake. You should be using Small Business Server 2003. It can accomodate up to 75 users (plenty for growth) and comes with lots of bells and whistles built in that 2003 Standard does not. (Including SQL in the Premium version). Here are the advantages of a domain.
1. File and network security. You simply cannot properly secure files in a workgroup. With a domain, you can get extremely granular in the files that are shared, who can access them, modify them, etc. With SQL, security is virtually impossible without a domain.
2. Active Directory. Enough cannot be said about this tool. It manages users, computers, printers and other devices... sets permissions, authenticates... it can be as simple or as complex as you wish to make it.
3. Group policy. You can ensure that all computers are up to date with the latest patches, etc. You can ensure that all have up to date virus protection. You can create logon scripts to map drives, share resources, etc. You can manage security, password policies, remote access policies, etc. Instead of managing each computer and user, you can manage them all as groups from one location.
4. Exchange. You can host your own e-mail, share calendars, access your e-mail, files and information from anywhere with any computer.
5. Routing and remote access. You can control who, where and when users can access your network remotely. Feeling sick? Remote web workplace lets you work at home just as productively as you could at the office. But Joe, who is a bit untrustworthy, can't download sensitive data to his home computer... ever.
6. Sharepoint services. A central location for sharing information with your workers, clients or prospective customers.
This is just scratching the surface. Asking the difference between a domain and a workgroup is like asking the difference between a biplane and a 747. Both will get you where you want to go... eventually. But in terms of comfort, convenience and additional features there is absolutely no comparison.