FWIW Freehand Painter strikes me as a PC version of a free Android app -- https://play.google.com/store/search?q=sketch -- http://www.amazon.com/s/ref=nb_sb_noss_2/175-0709280-1536505?url=search-alias%3Dmobile-apps&field-keywords=sketch
While Freehand Painter says in the help file that it is vector based, you don't get most of the advantages of a regular vector graphics app, though it is a lot less complicated than the average app in that category -- it's not so much that they're harder to use as much as they give you a tremendous number of additional options. Long ago drawing with a paint brush type tool in a vector based app was unheard of -- CPUs simply lacked the horsepower -- but for the last several years it's not only expected but sometimes expanded on quite a bit. That's not to say don't bother with Freehand Painter -- if you like it Cool -- but I can't help wonder if many people wouldn't have more fun installing Blue Stacks [ http://www.bluestacks.com/ ] & trying some of the Android apps above.
Microsoft's Expressions isn't bad, especially for free, but it isn't as easy to use & doesn't have as many useful enhancements as you'll find in a lot of other designer rather than developer oriented vector graphics software. It's not free, & it's a bit harder to find, especially on sale, but Corel has a Home & Student version of their flagship Corel Draw! suite that has Very few differences from their regular version. Inkscape is always free, & there's a portable version, but it falls shy of Corel's app [&/or Adobe Illustrator] by a pretty fair amount.
A regular rasterized image that's 300 x 300 pixels at the PC std. 96 dpi stores color data for each of the 90k pixels shown on screen. Note: rasterized images are like bean bag chairs -- they can be flattened to cover a larger area, or you can shape it so it's taller but covers much less space... an image at 300 dpi has more depth, but you don't see it, just like if you were looking at the very top of that beanbag chair, so you couldn't see how tall it was. OTOH you can take that same image & set the resolution to 96 dpi without re-sampling, & it covers a much, much larger area, but with ~ 1/3 the depth, same as if you jumped on & smooshed the beanbag. If you pay attention to that sort of thing it's actually harder to deal with today than it was years ago, since I think most developers gave up on people figuring it out, & so decided to try & compensate behind the scenes. Dpi matters when you print, so printing a 600 dpi image will look better than the same image at 300 dpi, which looks better than the same thing at 96 dpi, But, a lot of printers & software nowadays will try to compensate & make printing a 96 dpi photo look OK. Problem is when so many cameras take jpg photos with the default 96 dpi, those images take up this large viewing area, software often doesn't write jpg files to include any info on resolution [dpi], & people often wind up resampling those photos [intentionally or behind the scenes in their software], reducing the frame size but sticking with that 96 dpi, & if they print it, it doesn't look nearly as good as if they re-sized without resampling -- think of it as re-shaping that beanbag rather than unzipping it & dumping a lot of the pellets out.
A vector-based graphic stores points in their relative positions, & includes instructions on how to draw lines connecting them, their color, & how to fill any closed shapes. Where it gets to be more a PITA, there are different kinds of points, e.g. smooth points where the line coming in & the line going out look like one single line, or maybe you've got a corner point where the 2 lines form a corner like the name suggests. And each of these points has 2 handles, one for each line, & how far you drag them away from the point, along with the angle of dragging, controls the shape of the line, whether it's straight or some sort of curve. Most apps have primitive shapes like rectangles & squares & circles you can use instead, but originally vector graphics were drawn one point at a time, placing each point then adjusting the handles. When you use a paintbrush tool, an app like Expression Design calculates where the points should be added, drawing the lines connecting the dots. The big problem is vector graphics apps are so precise, most lines you'd draw look like a drunk walking across an uneven field, in a snowstorm. TO fix that they have various smoothing algorithms, they'll ignore any points closer together that the amount you set & so on, but it's a compromise -- the more loosely a line follows your actual drawing the better it looks, but the further it is from what you drew. There are also tracing apps, sometimes built into whatever vector graphics app, that turn a rasterized image into a vector-based graphic, & they have the same sort of trade-off, where you need to adjust the sensitivity for best results.
Because they're only instructions on how to draw something, vector graphics files are smaller, & vector graphics themselves can be scaled from the size of a postage stamp to a banner covering the side of a tall building, all without losing quality. And they're Very precise -- that's what CAD [drafting] & 3D apps use. Apps like Photoshop can use vector graphics based lines or paths while working with rasterized images. And vector graphics make up most illustrations in magazines -- generally if you see one or more absolutely straight lines, it was/is vector graphics.
