Within subjects examine variability "within" people (or subjects), such as each persons score on a repeated measure over time. By contrast, a between subjects design looks at differences between people (or subjects) on some construct. You can have a control and test group and then examine variability "within" group, or even within person if you have multiple time points of data collection, but once you begin comparing across groups (or even across people), your analysis becomes "between" subjects. I hope that helps!
I'm curious what is the difference between a within-subject and between-subject design. I know that within-subject designs every participant receives all the treatments where as a between-subject design is compared to a control group. Can there be a control group with a within-subject design? I'm confused with the AB/BA format....