Those two rule types both use quantity ranges to setup different pricing, but even though they are really similar, the calculations are made differently.
In Tiered Pricing, you get the increased discount only for the extra quantity unit(s) added on top of previous range, when Bulk Pricing allows to set discount for the whole amount.
Here's the example:
|1 - 23||0.44|
|24 - 99||0.35|
With Tiered Pricing such prices works like that:
1-23 gets 0.44 price, and 24-99 gets 0.35, so for example, if you buy 50, the average price in cart is (0.44*23+0.35*27)/50 = 0.39 and that is reflected as cart item's average price.
But in Bulk Pricing, if 50 is purchased, it will be 0.35 per each item.