Stress is the force carried per unit of cross-sectional area inside a material, while strain is the proportional amount that material stretches or compresses under that stress. Confusing the two obscures that a thin rod and a thick rod of the same material fail at the same stress but very different total loads.
Young's modulus measures how much a material deflects under load (stiffness), whereas strength measures the stress at which it breaks; the two are independent properties. A material can be very stiff yet weak, or flexible yet strong, so a structure can fail either by breaking or by deflecting too much to be usable.
Any loaded structure stores energy as it deflects, like a spring, and this stored strain energy is what drives cracks forward when something breaks. Whether a structure is safe depends not just on peak stress but on how much energy is released if a crack begins to run.
Stress is not spread evenly through a material; it piles up sharply at the tip of any crack, notch, or sudden change in shape, reaching local values many times the average. A small sharp crack can therefore cause failure at loads far below the material's nominal strength, which is why real materials break well before theory predicts.
Every structure can be read as a system managing two opposite jobs: resisting being pulled apart (tension) and resisting being crushed or buckled (compression). Materials and shapes good at one are often poor at the other, so structures combine them, as ropes handle only tension and masonry arches only compression.