It's hard to tell the difference between a created vexel and a vector. This is because they are not a style of art, but a medium of art.
When we say a "medium" we mean with how a piece of art is created or what with. For instance we have both traditional and digital paintings. A traditional painting is created with, for example, oils and water colours. however a digital painting is created with, for example, you use a paint brush tool or smudge/dodge/burn tool. Although the end result is the same, it's what it's been made with which is the key difference... and especially how we categorize it on deviantART.
Vexel art: created using raster layers.
Vector art: created using vector layers.
It's easy to remember vectors are made with vector layers... but to associate vexels with raster layers is a little less easy.
The word "vexel" was created based on work appearing to be vector art, but was on raster layers which consist of pixels.
Ok, this is a little exercise you can do to show you the difference.
1) Right click on your own avatar and save it to your desktop.
2) Open it in your graphics program of choice.
3) Zoom into the image as much as you can... well maybe until about 500%
Below is the example avatar zoomed in at 500%:
Looking at your avatar you can see how it is made up of coloured squares. These squares are pixels and show that your .jpg/.gif or .png file of this image is on a raster layer.
1) Now zoom back to 100%
2) Go to Edit > Resize or Image > Resize --- or which ever way to resize the image size.
3) Increase the size to say 500% of the original size
Below is the example avatar resized in at 500%:
Depending on the program you have used, you will either see the coloured squares... or you may see a big version of your avatar but with blurred lines and not as sharp as your original sized avatar.
In the first image, your art program read the file and the file told it that for each single pixel in your avatar, it wants it to be a specific colour and in a certain place.
When you resize it, your art program tries to do the best it look as smooth as possible when the size is increased... and to not make the image look pixelated.
