Well "The thicker a beam is, the stronger it is" is very vague. It doesn't express the relationship between thickness and strength very precisely. For example, does it mean exponentially proportional? Increasing the thickness a LITTLE may increase the strength A LOT. This is exponential proportionality.

However, the 2nd statement is a statement of direct proportionality. If strength = S, and thickness = T, then the 2nd statement says where k is some constant! This means that if you change S, then T change proportionally!

So all in all. The first statement does not specify how proportionally one variable changes to another, but the 2nd statement does!