Stiffness and strength are different properties
Two things routinely confused, and the failures that follow.
Stiffness and strength are different properties because stiffness describes how much a part deflects under a given load, while strength describes how much load a part can take before it actually breaks, and a part can be extremely good at one of those two things while being unremarkable, or even poor, at the other.
How far it moves against how much it takes
A stiff part resists changing shape, springing back to where it started the moment a load is removed. Stiffness describes how steep the relationship is between how hard something is pushed and how far it moves in response, and it comes almost entirely from the material's Young's modulus and the part's shape. A strong part resists failing, whether by snapping, tearing or permanently bending, and strength describes how much load it can absorb before crossing that line, which can have little to do with how far it moved on the way there. A part can therefore be flexible and strong at once, deflecting a great deal without breaking, or stiff and weak at once, barely moving until the moment it snaps.
A rubber band and a breadstick
A rubber band stretches to well beyond its own resting length before it breaks. It offers very little resistance to being pulled and deflects enormously for a modest force, yet it tolerates all that stretching without failing, which makes it soft but tough. A dry breadstick is the opposite combination: it barely bends under a pushing force and feels rigid right up until it snaps, with almost no bend beforehand, which makes it stiff but brittle. Calling either one simply strong or simply weak misses which of the two properties is being described. A rubber band round a parcel relies on exactly its combination, the low stiffness letting it stretch snugly round an awkward shape while its strength keeps it from snapping under that stretch.
Why steel makes the two look like one
The confusion usually starts with ordinary steel, which is reasonably good at both, making it easy to assume the two always travel together. They are set by different features of a material's internal structure. Stiffness depends on how strongly the atoms resist being pulled slightly apart from their resting positions, and heat treatment barely shifts that. Strength depends on how easily those atoms can be made to slip permanently past one another, which is exactly what heat treatment changes. A hardened alloy steel can have four times the yield strength of plain mild steel, yet a bar of each, loaded gently, bends by almost exactly the same amount. Changing a part's shape works the other way, adding stiffness without necessarily adding strength.
Springs and crash structures
The distinction becomes impossible to ignore when a design needs one property without much of the other. A spring must be strong enough not to deform permanently under repeated loading, yet it is deliberately made far less stiff than the structure around it so that it can flex and absorb movement. A crash structure is deliberately made weak in a controlled, predictable way, so that it absorbs energy by crushing instead of passing the full force of an impact through to whatever it protects. Assuming a higher figure for one property means a better figure for the other would produce a spring that does not spring and a crash structure that does not crush. Asking which of the two a part needs, before reaching for a stiffer material or a stronger one, is the habit that avoids both.