Perhaps the easiest way to answer your question is to start from a slightly different place. We need to distinguish the idea of rights from the idea of what is morally right (and wrong). Once we’ve made that distinction, we can then look at the further distinction between what is morally wrong and what is morally bad.
The idea of rights extends widely. I have a right to go to the cinema, a right not to be killed, a right to be paid (given my contract with my employer), a right to have children, a right to the exclusive use of my house. Some rights are moral rights, some are legal, some are the results of contracts. In general, a right can be understood as an entitlement to perform, or refrain from, certain actions and/or an entitlement that other people perform, or refrain from, certain actions. Many rights involve a complex set of such entitlements.
The two central features of rights are:
Privilege/liberty: I have a privilege/liberty to do x if I have no duty not to do x. I have the right to go to the cinema because I have no duty not to go to the cinema. But I have no right to steal, because I have a duty not to steal.
Claim: I have a claim right that someone else does x in certain cases in which they have a duty to me to do x. Claim rights can be ‘negative’ – they require that other people don’t interfere with me (e.g. the right not to be killed); or ‘positive’ – they require that other people do specific action (e.g. the right to be paid if I’m employed).
While every claim right entails a duty, not every duty entails a claim right. Some duties are based on rights, but some are not. I may have a duty to give to charity, but I have not violated anyone’s rights if I don’t. So talk of rights should not be confused with talk of what is morally right. And so I’m afraid we can’t simply say that because something is morally wrong, you have a (claim) right that it is not done to you. In the example you give, I would suggest that it is wrong to kill someone from a distance for pleasure because people have the right not to be treated this way. It is not that you have the right because it is wrong. The fact that it is always wrong (let’s suppose) doesn’t mean that it is based on a right, either. For instance, you have certain property rights, which make it wrong for people to take your property from you. But there are circumstances in which this is not true, e.g. forced purchase by the government, or commandeering your car in a police emergency. The system of property rights is not absolute, but it is a system of rights nevertheless.
So to ‘wrongs’ and ‘bads’. We often associate rights and wrongs with duties, esp. duties of justice - to do with minimally required treatment of others. Actions which do not violate a duty can nevertheless be bad. Exactly which actions qualify depend on your theory of duties. But some suggestions might include squandering opportunities to do good, failing to show kindness in a personal relationship, or other matters related to personal virtue, moral development, and seeking the good of others.
There’s much more to say about all these matters, but I hope that helps!