Q: What is meant by "professional"? What is the difference between a "website" and an "online business"?
A: An online business has three parts - branding/identity (how a site looks and represents you), its ability to bring in new customers and retain current ones, and its support for operations, such as event management, corresponding with customers, document management, etc. Professionals will implement all of these aspects so that you get business value in return (not only increased revenue but also lower administrative costs and mistakes). With amateurs, you'll usually get a pretty site (from the artistic types) with little business value, or a frankenstein site (from your "genius nephew") that does nothing for your enterprise but glues you to the hip of your technology guy. If you value your investment, it's critical to know the difference.
Q: Why should I care about the platform, such as Joomla, or HTML/Dreamweaver, or Wordpress, or Cold Fusion?
Because of higher costs and vendor lock-in. Neither are in your interest, so ask and be picky.
Q: OK, what are the main differences between them?
If you're blogging, Wordpress is easy to use and free. You can learn it in a couple hours and don't generally need any technology assistance. Highly recommended for those who mostly use their site for blogging or identity and high-end graphics design.
HTML sites made by artistic types using Dreamweaver are often eye-catching but return negative value in general. They only solve the identity issue and are very poor on business value and ability to bring new customers, etc. Furthermore, they lock you into the person(s) doing the site, because everything is in pages and technical code. Extending functionality is done by amateurish links to paid services such as Constant Contact, and the data gathered is not under your control, nor is the site integrated to your business. Not recommended.
Drupal is the leading open-source (free) content management system for high-end businesses. The learning curve is high, and the start-up costs are high, but the scalability costs are minimal if you intend to scale your operations into the hundreds of thousands of users/transactions. Recommended in CAPEX-intensive situations.
Joomla runs almost 3% of the web and is the fastest-growing platform in the past five years for good reason. It is open-source (free), as easy to use as Wordpress (approximately the same learning curve as MS-Word as one example), is more easily extensible than other platforms, and has a vast selection of add-ons (e-commerce, document management, etc.) at little or no cost many times greater than those available for other platforms. Highly recommended for SMBs, non-profits, and local government agencies.
Q: What should a website cost?
If you're building an HTML site, in 90% of the cases you'll get less than what you pay for. If you buy a site for less than $1000, then you are throwing your money away. If you are paying a monthly fee for website development, then your true costs and actual value-return are hidden. For good reason.
If you're building a site in Wordpress (blogging), Joomla (SMB's, non-profits, etc.), or Drupal (large-scale online transactions), you'll get more than what you pay for in 90% of the cases, because the software and much of the labor is discounted, and your costs are funnelled into real function and content rather than re-inventing some technology wheel.