What makes black pepper strong or mild?

There are really only two main varieties of black pepper, Tellicherry and Malabar. They are processed the same, and in general (though you might tell a difference in a side by side comparison) have the same flavor profile. What could easily change the flavor and/or "spiciness" is freshness of the spice, and the grind (both how coarse/fine, and how recently the pepper was ground). Further, heating the pepper in a pan before grinding, also brings out more flavor. It also turns out that terroir is a factor in the flavor and aroma of pepper. So, where your pepper comes from certainly impacts your experience. The coloration is simply a composition of the inside and outside of the seed itself when it is ground and mixed.

Peppercorns are a small fruit. When processed, the green skin turns black and the flesh of the fruit remains white. Both the skin and the flesh contain piperine, which is the chemical that causes the heat of pepper. Wikipedia that black pepper is about 5–10% piperine and white pepper slightly more. It doesn't say how much more, so I assume the difference between black and white pepper is smaller than the variation within black pepper.

It's possible that specialist sellers will have hotter and less-hot peppers. Other points are:

1. Don't use pre-ground pepper. The exposed surface of the ground pepper starts to lose flavour compounds, by evaporation and chemical decay, especially if it's finely ground. As with any spice, freshly grinding it yourself will give the most flavour.

2. Grind size is important. Finely ground pepper will release more flavour because it has much more surface to transfer that flavour through. On the other hand, coarsely ground pepper will give you those little hits when you bite into a chunk. It might even be best to use both: fine-ground for background and coarse for the zings.