What is the difference between Selenium IDE and Selenium RC with its functionality?
Selenium IDE is a firefox plugin that gives you a basic recorder for recording tests. These tests are recorded in an HTML table based architecture using keywords, and IDE gives you the ability to then export the code out to other languages (Java, .Net, PHP, Python, Ruby, or Perl).
Selenium RC is an API accessible from multiple languages. Rather than recording tests, you write programs that call into the API to control the browser.
You didn't ask, but Selenium WebDriver is Selenium 2.0's equivalent of RC. It's an API that is called from whatever language you're using (I believe it supports Java, .Net, Ruby, Python, and PHP_. This is a different API than that used in Selenium RC, but there are compatibilities built in to make the transition easier.
Most people find that having a full programming language available like you do with RC/Webdriver gives them much more power and flexibility. For example, conditional statements like if thens or loops are much easier to do in a programming language than in the HTML tables that IDE works with. Selenium 2 has just been released today.
I haven't used IDE in a while, but from what I remember, most of the actual API that Selenium provides is available in both the HTML keywords and the API functions, but the API is far easier to work with and make tests beyond the simpler ones that are recordable.
There's more information available at http://seleniumhq.org