Systems Dynamic is like performing surgery. Systems thinking is like a first aid kit. Dynamics work with simulation and mathematical patterns representing intangible relationships. The strength of your simulated model comes from how much you test flow rates to produce emergent behavior. Systems thinking is more like systems psychology. You have a number of archetypes and see which one fits your system best. Then you have counter measures of each archetype.

I think Jay W. Forrester provides a good starting point for understanding the differences:

From J.W. Forrester (1994) System dynamics, systems thinking, and soft OR. System Dynamics Review 10(2-3): 245–256.

"System dynamics, systems thinking, and soft operations research (soft OR) all aspire to understanding and improvement of systems. In all, the first step interprets the real world into a description used in following stages. In system dynamics, description leads to equations of a model, simulation to understand dynamic behavior, evaluation of alternative policies, education and choice of a better policy, and implementation. Case studies, systems thinking, and soft OR usually lack the discipline of explicit model creation and simulation and so rely on subjective use of unreliable intuition for evaluating the complex structures that emerge from the initial description of the real system. Nevertheless, systems thinking and soft OR, with emphasis on eliciting information from-real-world participants, should contribute useful insights to system dynamics. Conversely, the model creation and simulation stages of system dynamics should contribute rigor and clarity to systems thinking and soft OR."

One is a fraud, the other isn't. Systems thinking, unless you went to MIT, is a cognitive paradigm and useful in virtually any endeavor. If you went to MIT or read Forrester, Sengé, Richmond, et al. then systems thinking is system dynamics. Meadows wrote some useful concepts, but she was the exception in that crowd. The thing they don't tell you in their books is that system dynamics is a very limited, almost useless modelling tool that looks really cool, but can't be modified easily to reflect change or non-linearity. In other words, both the bias and the variance of the model are very high. The verification may be reasonable, but the validity tends to be bad.

Some examples of this failure: Jay Forrester's World Dynamics. I encourage you to read the reviews such as "Measurement without data." Peak oil. This was a system dynamics model crafted at great expense by some really smart economists and petrol-heads and predicted world oil production would peak about 15 years ago. Didn't happen. In fact production is up far beyond the simulation. So, what good was the system dynamics simulation? not much.

For a good insight on what systems thinking really is and how it is useful, check the work of Russell Ackoff. He has some good lectures online. C. West Churchman was his graduate advisor I believe, also worth reading.