Here are descriptions of bitmap images and vector images. There are several sites on the web which have some examples and explanations of each type.
Bitmap-based images are comprised of pixels in a grid. Each pixel or "bit" in the image contains information about the color to be displayed. Bitmap images have a fixed resolution and cannot be resized without losing image quality. Common bitmap-based formats are JPEG, GIF, TIFF, PNG, PICT, and BMP. Most bitmap images can be converted to other bitmap-based formats very easily. Bitmap images tend to have much large file sizes than vector graphics and they are often compressed to reduce their size. Although many graphics formats are bitmap-based, bitmap (BMP) is also a graphic format.
Vector images are made up of many individual, scalable objects. These objects are defined by mathematical equations rather than pixels, so they always render at the highest quality. Objects may consist of lines, curves, and shapes with editable attributes such as color, fill, and outline. Changing the attributes of a vector object does not effect the object itself. You can freely change any number of object attributes without destroying the basic object. An object can be modified not only by changing its attributes, but also by shaping and transforming it using nodes and control handles. Vector graphics are resolution independent because they can be output to the highest quality at any scale.
You can create your own vector patterns but you would graphic editing software to do it. Photoshop does have some vector graphics in it. Again, there are tutorials on the web which tell how to do this. Here is just one tutorial about how to do a vector drawing in Photoshop:
Vector Tutorial
I hope this helped explain the difference between the two.