There's a book for Engineers, entitled: 'Roark's Formulas for Stress and Strain', some describe it as 'High level Mathematics'. So what?
Underneath the formal definitions, the intuition is
- stress is what you do to a material;
- strain is what it does as a result.
To a first approximation they are connected by Young's modulus, which obviously varies a great deal by the material.
You can put two materials under the same stress (one industry standard elephant, say) and the the strain will be very different depending on the material (steel might exhibit less strain than rubber, for example).
Alternatively, the same strain (eg 10% lengthening) is achieved with different stresses depending on the material (eg stress of one mouse per square inch for rubber, stress of one elephant per square inch for steel).
As you can tell from the intuition above, stress is measured in pressure (force per area) and strain is dimensionless (just a proportion or percentage, or whatever).