Luckily the forum is using Georgia typeface, so both can be easily shown below:
a vs a
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Well, I suppose you can pretty much get your answer by considering how you managed to generate the two different forms in your post - a normally occurs in italic fonts, whereas a is more normal in standard print fonts.
The italic form is just easier to use in handwriting, I guess. Similar flourishes and such occur in the "print" form for other letters - many fonts have a particularly ornate lower-case g that you normally wouldn't try to reproduce by hand.