You know which one Real Madrid chose.
This is a new injury, or at least a development of one. Bale cleared his medical with no noted issues. What Bale is dealing with now is a muscle contracture.
This is a common but complex injury where the muscle or its associated tendons are physically shortened due to a number of possible causes. It's most often seen in muscles that have been immobilized for a period of time, which certainly isn't the case for Bale. The result is a loss of range of motion and likely some muscle weakness or loss of function.
While I don't want to get too technical here and have to explain sarcomeres, Krebs cycles and the other minutae of muscle function, suffice it to say that Bale is a well-developed adult male with largely normal function and overall fitness. This leaves the most likely cause the result of a muscle imbalance that has led to a period of spasticity.
In simple terms, he has a chronic cramp that is causing the muscle to be shortened, leading to problems with range of motion and antagonistic strength.
All of these things can be corrected, but not quickly.
While Real Madrid has said that Bale is definitely out for Wednesday's Champions League match, but the progress or lack thereof with treatment could have him out much longer. Sky Sports reported that Bale's participation in World Cup qualifiers with Wales is in jeopardy. Those matches come up mid-month, giving some short-term expectations that Bale will miss more than a single match.
The most likely treatment is a gradual use of stretching, modalities such as electric stimulation and a graduated return to function.
Real Madrid's medical and sports science staff have no lack of resources or options at their disposal. They could even use a contracture correction device (CCD), which is essentially a machine that creates a very slow stretch or "creep." This type of device has to be purpose built and closely monitored.
There's a bit of a push-pull for Bale. He's clearly a valuable asset, one that must be both showcased and protected. One element of the team will want him back quickly to show that the signing was worthwhile. Another element will want to be very cautious so as to not cause further damage to his valuable legs.
Finding that balance is going to be a tough task and one that goes well beyond the medical question.
The team does have enough depth to give the medical staff time to do its work. While Bale makes Real Madrid (or any club!) better in the immediate, Real Madrid is going through an adjustment period regardless of any injuries or absence.
Getting Bale back on the field should be a secondary concern to his long-term viability and keeping his skills intact.