I recently had the pleasure of making a logo for Front & Centre - Eddy and Gabi's radio show on SYN, to be used on their Facebook page. Just by the way, you should definitely check them out! Here's their Facebook page - or you can catch them on 90.7 SYN FM at 3pm on Thursdays.
Now, I'm not a professional graphic designer by any stretch of the imagination - though at one point in my life I even wanted to be one - but as a favour I'm always happy to mock up something simple.
Eddy's request was "just an F and a C, maybe in a box". Pretty straightforward and simple. For a bigger project I might start drafting ideas on paper, but as this was a simple request, I dove straight into Adobe Illustrator.
Why not use Photoshop? Well, for something like a logo what you generally want is clean geometry, right? Warning: awful explanation incoming. (scroll down a couple paragraphs for the TL;DR) So, Photoshop is great for complex, detailed images and in particular what's referred to as rasterised data. One way to think of it is that when you take a digital photo, it is what it is - a bunch of pixels, and each individual pixel represents a particular colour and they fill a certain set of dimensions, like 6000x4000 which is 24 megapixels. However when you zoom in on your image beyond its maximum size, you cannot create any more detail because what's there is just what's there.
Illustrator on the other hand almost exclusively controls vector data. Instead of dealing with pixels which are limited by resolution, it basically uses location information. It's kind of like if you took a bunch of points that are GPS pinpointed on a 2D surface and then joined them together with lines and curves. You can zoom in or zoom out, but that position doesn't change. A pixel would begin to appear bigger or smaller, and the space between the pixels would scale with them. Vectors don't change like that. While Photoshop does have limited vector functionality, Illustrator manipulates them on another level.
Anyway, TL;DR: Illustrator is great for vectors, and vectors are great for making clean shapes you can resize to any scale you like. Like with logos.
So, back to the logo. The initial request was simple enough. Basically I picked a font, changed the weight and size and typed "F" and "C". Wow! Given that this isn't a commercialised project I wasn't too concerned about typeface licensing.