The Institute of Medicine gave us a definition of Quality as noted below.

In some ways this is a helpful way to think about what quality health care should mean, particularly from the perspective of a patient. Who would not want their care to be all of these things? And why would health systems not strive to achieve all of these things for those that they care for?
Yet, in this conceptual model, you can see that safety is a subordinate element to quality. Further, this model suggest that you can have all of the elements that make up quality at the same time. This model suggests that health systems can have it all and if you are not successful, it’s hard not to feel that there is something wrong with you since a bunch of brilliant people came together to come up with this model. Those smart folks certainly seemed to think you should be able to do all of these things successfully!
I don’t mean to be a naysayer, but I don’t think you can have it all. Even great systems with plenty of funds might struggle to achieve all of these things. With this in mind, I prefer a different way of thinking about quality and safety.

In the above model you can see that Safety and Quality are now co-equal elements with the other elements seen as a continuum between the two key areas of quality and safety. So now what is the definition of quality versus safety? I believe safety is all the things that should never happen to a patient, while quality is all the things that should happen to a patient. What does this really mean? Well, a patient should never have an operation on the wrong part of the body (this is a safety issue). On the other side of the continuum, a patient should always get the medication they need at the time they need it. Put another way, when a safety problem manifests (a facility cuts off the wrong leg) someone may well lose their job because everyone looking at the error (including the average person on the street) is appalled and feels like such thing should never occur. If your facility quality isn’t that great, you might eventually lose your job, but it will take some time (because who doesn’t except crappy food in a hospital?).
In the above model, the other elements such as timely care, effective care, etc are a continuum between safety and quality. This model better shows the tension that can exist between the various elements and it can also suggest how problems can develop along the spectrum. As an example, efficient can be in tension with patient centered care if the patient feels rushed. This model reminds us that a focus on efficient care, if done by cuts and demands for harder work rather than improvements in the actual work, might gain in quality for a time but might ultimately cut so many important things that a sudden unexpected catastrophe occurs. In hindsight it may become clear what happened, but without the focus on the various tensions that this model helps people consider it can be very hard to anticipate the ways things might go wrong.
I think it is important to consider a few things with this model. First, safety and quality are like two sides of a coin. Each face is distinct, but where the middle of the coin changes from one face to the other isn’t clear. This is true of the middle of this model. Where the continuum of safety changes more toward quality isn’t clear. Further, it is important to consider that the patients want it all. They want us to try very hard to give them both a safe environment as well as high quality care.
A last point. I have often been challenged in this model in that how is it possible to ever have a quality experience that isn’t safe. Consider this scenario. A patient comes to the Emergency Department and is diagnosed with a significant pneumonia. Their wait was short, the nurses attentive and they are admitted into a nice room with a nice warm meal arriving shortly after arrival. Yet, the system has ignored a problem with the bar scanning system that helps track medication administration. Nurses have complained about this vulnerability but it really hasn’t seemed to cause problems so the hospital, concerned with costs, has not addressed this issue. It turns out there was an error in how the medication was ordered and the patient gets too much causing an injury to their kidney. A properly functioning bar scanning system would have helped prevent this adverse event. The patient was in a system that had a safety problem but they thought the quality was just fine.