I'm trying to find a daily stretching routine to incorporate in addition to my cardio and resistance training. I understand that flexibility is not necessarily the same as mobility. I was wondering if anyone could offer examples of how two routines/programs would differ with these competing focuses?
The difference in flexibility vs mobility is flexibility stretching can keep your muscles flexible and elongated. For instance, if you do not stretch as a bodybuilder then you end up not being able to touch your toes or to reach behind your back, etc. Mobility training does not affect your flexibility but can help correct a curved spine, allow you to move your hips better or rotate them, rotate your shoulders fully and more. Stretching for mobility also benefits your flexibility.. but stretching for flexibility does not necessarily help your mobility. Note that specific to your question, there is also a difference between mobility stretching and mobility dynamic exercises where you are actively moving but it is not considered a stretch.
Here are examples of stretching for flexibility: Yoga poses such as downward dog, stretching your hamstrings, stretching your triceps, really any yoga poses you can think of.
There is also dynamic stretching such as opening your hands wider and wider to stretch your chest, arm circles, jumping jacks.
You can also foam roll a muscle to stretch it out or relieve tension in a tight muscle to some extent.
Stretching for mobility: Thoracic extension stretch on a foam roller, thoracic rotation with open book exercise, band pull aparts
Dynamic mobility exercises: Hip rotations, Cuban presses, external and internal band rotations, squats with a 90 degree rotation, clamshells
Mobility training is just as important as stretching. If you are not playing a sport or doing much that trains your mobility naturally I would also add some mobility moves in with your stretches. Rotator cuff exercises are part of mobility training and deserve a place in your workout.
"I'm trying to find a daily stretching routine to incorporate in addition to my cardio and resistance training..."
Unfortunately, there are no decent stretching routines available to the public. Stretching has been terribly neglected in the fitness space. I stretch everyday for between one and two hours, and I had to develop my own routine. You will also have to develop your own routine. To help you get started, here are a few tips:
1) Here is an absolutely fantastic stretch for the external rotators of your hip (e.g. Obturator Internus). It is a shame nobody knows about this one.
2) Here is a fantastic stretch for your hip flexors.
3) There is some scientific literature on stretching the internal rotators of the shoulder for baseball players. Please note that the Cross-body stretch is now out of date and has been replaced by the Sleeper Stretch.
A couple other points:
1) The closest thing to a well rounded stretch program that I know of is "Stretch Therapy" by Kit Laughlin, who is out of Australia. I don't do his routine myself, so I can't tell you whether it is good or not, but it is worth a try.
2) There are now some franchises that do nothing but stretch, such as Stretch Lab. It looks like Stretch Lab has about fifty locations around the US. The downside here is that they require a personal trainer and they are expensive. I haven't done Stretch Lab myself, but I intend to do this soon.
3) Never take stretching instruction from someone who was flexible at an early age. These people have no idea how a stiff adult body works because they have never been in this situation. Kit Lauglin says this all the time. I can tell you first hand experience this is true.
5) When you see pictures of people stretching on the internet, be aware that most of these people are genetically hyperflexible. What they are doing may look good in the pictures, but it probably won't work for you (unless you are also hyperflexible).
6) If you mention "stretching" to most people, they think of Yoga. However, Yoga is not stretching. For example, the three stretches I referenced above (the Sleeper Stretch, external hip rotator stretch, Hip Flexor stretch) are not part of Yoga. Point is, that many great stretches aren't practiced in Yoga.