I tend to find that groin pain isn’t that common in runners, or at least road runners, unless they compete in other sports where sideways or kicking motions are required. Cross-country or off-road runners may be a little more at risk of groin pain due to the less uniform backwards/forwards movement pattern.
The adductors are better known as the groin muscles. As covered elsewhere, tendinopathy is an umbrella term to cover all forms of overuse (gradual onset) tendon pain.
In cases of adductor or groin tendinopathy, a pain is usually felt in the inner thigh, high up near the pelvis. The pain develops gradually and not from one sudden movement or action. The more you continue to run on it, the worse it will get. It will feel tight when moving the leg out to the side and usually stiff in the mornings.
Treatment involves rest from running and anything else that aggravates the condition until pain free on a daily basis. The only self-treatment I would recommend is lots of gentle stretching of the groin and hip muscles. There are lots of nerves and blood vessels in the vicinity of the groin muscles and so I don’t recommend poking about in there too much yourself. Visit a sports injury professional for treatment.
There are five groin muscles which could be affected in this case. In my experience, I have found that the most commonly injured of these in runners (who only run) is the Pectineus. This is actually one of the smaller groin muscles and it can be injured through over-striding. Lengthening your stride to attempt to speed up may cause a problem for this muscle.
If you do have a Pectineus injury, the pain will be located right in the crease at the front of the hip. Feeling around in the large groin tendons right on the inside of the thigh doesn’t usually cause any discomfort. Move outwards slightly, to the front of the hip along the line of the crease and this is where the Pectineus muscle can be felt. Tenderness here is a pretty good indicator of injury. There will also be some discomfort on adducting the hip (bring the leg inwards towards the other leg), especially when the knee is bent as this takes out the longer groin muscles. Adduction with flexion and a bent knee is the most painful movement.
Again this injury is best treated by a professional therapist. Massage techniques are usually successful, but it is a complex area with numerous nerves and blood vessels which could be damaged by untrained hands.
The best thing you can do is rest from anything which aggravates the problem and gently stretch the entire hip area. Strengthening exercises for hip stabilisers and core muscles are generally a good idea, to provide a stable base for muscle attachment. When returning to running, take shorter strides to reduce stress on the muscle.