It comes down to the job and the power of your circular saw…
If you’re new to woodworking and would like a one minute overview of the differences between circular saw blades check out this video with Tim Carter of http://www.AsktheBuilder.com.
To get a bit more depth on matching saw blades with your job, check out How to Choose the Right Circular Saw Blade.
And for a discussion of the differences in usage between full kerf and thin kerf I suggest the full kerf/thin kerf discussion in WoodNet.
(Kerf is the width of the cut as determined by how wide the teeth protrude on the blade.)
And if you really want to dig into the history of saws I highly recommend the wikipedia Saws page.