What's the difference between 'research topic' and 'research area'?

A research area is what a research topic is placed into, but is much broader than the scope of the topic. For example a research area can be human physiology, computer science (as you mentioned) or even relate to a specific field within these broader terms such as cardiac electrophysiology or machine learning respectively.

A research topic would be a specific question, hypothesis or problem you wish to investigate and answer which is under the scope of your research area. That is to say, my research area is in neuroscience/neurophysiology and my research topic is investigating the mechanisms of neuronal communication, as an example.

You would want to say topics that interest you which relate to a certain problem that you may be aware of, whereas in the research area you would want to outline your inclinations towards a particular field of academia.

While a topic is narrower than an area (for example, your area may be "solid state physics" and your topic "semiconductor tuning based on dopage"), it's probably true that for most people there is little difference between the two terms as far as colloquial usage is concerned.

In other words, don't obsess about the difference -- though, if you want, consider the "area" a broader term.