According to St. Augustine, an evil is a privation of a due good. This makes for an asymmetry between goods and evils: there are due goods and non-due goods. For instance, the ability to run a mile in less than 3m 45s is a good, but it need not be a due good. Those who have that ability are well off for it, but, plausibly, while the vast majority who lack it are less well off for the lack, the lack of the ability is not a harm or bad to them. (Maybe this example doesn't work, because maybe before the Fall we could all run really, really fast or something like that. The example is only illustrative.) So, on Augustine's view, while there are due goods and undue goods, there is no similar distinction between the evils (or bads—to my knowledge Augustine does not distinguish the two), as all evils are opposed to due goods.
This asymmetry thesis for evils is plausible independently of the Augustinian view of evil as a privation. Among the goods, there is a distinction between due goods and what one might call supererogatory goods. There is no such distinction among evils. We might say that the distinction between bads and evils is such a distinction, but I am sceptical of that distinction when people make it. The good/evil distinction seems to basically line up with the distinction between non-moral evils and moral evils or maybe the distinction between minor evils and major evils. Besides, the distinction seems to me to be an accident of English. (For instance, the Latin malum covers both, as does the Hebrew ra` and the Polish zlo.) Moreover, even if there is a distinction, it does not cut the relevant way. A runner who can't run a mile in 3m 45m is not a bad runner.
Here is one minor reason the distinction matters. Tooley when trying to calculate the probability that a given evil has a justification assumes that an action is a priori as likely to have a wrongmaking property as a rightmaking one. However, if there are three basic axiological properties: supererogatory good, due good and evil, then plausibly there are three kinds of "-making" properties of reasons corresponding to these, two of them positive and one negative, so a priori an action is twice as likely to have one of the positive ones than the negative one in the Carnapian probability scheme he adopts. Basically the point is that "rightmaking" really should be "permissiblemaking" in Tooley's context, and there are two significantly distinct ways a property could be permissiblemaking: it could be dutymaking or merepermissiblemaking.