Firstly, yes there is a difference and quite a big one. Each one has pro's to them, but maybe you should be focused on one more than the other.
Most injures are manifested from either too much or too little flexibility or mobility, and both are a huge factor in overall body movement and increased athletic performance.
One healthy meal doesn't make you thin, and one bad meal doesn't make you fat. Same is said for stretching, 1 yoga or stretch class a week, is sadly going to make very little impact on your flexibility or mobility. This is a subject that should become even more important than running, biking, lifting weights, and should be programmed in as a workout or training session like al of the other sessions you do.
Workshop agenda (mainly practical)
What is the difference between flexibility and mobility
Pro's and cons of each
How often should we do them
Mobility class 1
Flexibility class 1
Mobility class 2
Flexibility class 2