One of the key terms is 'impact', that infers high strain rates (100-100,000 time higher than tensile testing).
In some applications very high strain rates (in the millions or higher).
Under impact conditions you can measure various parameters, though total absorbed energy is the most common. You cannot really distinguish between toughness and strength.
Once you get into fracture mechanics they are many different characteristics. This covers fatigue (which mode, what load, what frequency) and what you measure (crack growth rate, energy to propagate) and if you start with precracked samples or not.
This is a very large field of study.
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P.E. Metallurgy, Plymouth Tube