When the average person speaks of karma, at least in the west, the concept they have in mind is that karma is a punishment and correlate it mostly with karmic law. What karma is though is not a punishment but rather a consequence. Don't get tripped up by the wording, they are different. A consequence is simply a result. A punishment assumes there is an entity doing the punishing. So at least for me a major differentiation between the two right away is that the western monotheistic religions have sort of crudely bent karma into their belief system where the idea that there is someone or something that is doing the punishing and keeping track of all the karma is a very silly concept indeed. It basically takes the high minded concept of karma and dwindles it down into some sort of Santa Claus with a naughty and nice list. Now largely this is my take on karma, not THE take. Feel free to offer your thoughts and comments on the differences, similarities, what you agree with or don't agree with. I'm not really religiously affiliated with karma, but have an understanding of it in terms of Hinduism and Buddhism as well as it's various form and definitions as well as the western interpretation of it.
Simply put, karmic law is the idea that what you do directly results in what happens to you. In some sense this is true, but in others it is not.
While I wouldn't say to explicitly live by karmic law, it has its merits. Logically it makes that if karma were a moral currency, when you deal out negative karma you will receive negative situations to balance your karma out again and vice versa with positive action. Religious views of karma can sometimes extend karma over lifetimes via reincarnation and sometimes believe that your current life's karma will directly correlate with how great your next life is. The problem with this belief is that karmic law is not punishing or rewarding you for your doings, but rather dealing out consequences. This is more theoretical and logic based, a set of defined rules that can be applied, but only arbitrarily to a very abstract concept because karma isn't really a strict inflexible rigid set of laws. This largely relies on causality which is to say that one thing is the cause of the next and so on and so on.
I'll give an example and dissect it
Someone feeling rather malicious, tries to steal from you and then runs into traffic in the panic of the situation and gets hit by a car.
This is instant karmic balancing, but this was not because the universe demanded it as so. It definitely feels that way for the two people involved however and this is why many people feel that karmic law is somewhat relevant. HOWEVER in the long term scheme of things there are usually more situations where you say why is this happening I didn't do something wrong to deserve this. If you assume that you can't have bad things happen to you for being good, are you really good or just avoiding the bad? In a more religious sense, some may argue that you are being punished for past lives. Again though, who is the punisher? You can probably always find a way to rationalize it, but realistically it doesn't make total sense.
One other thing to quickly touch on....
Free will when talking about karmic law can be argued both ways. You could say because that person has bad karma I as a good person must punish them. You could also argue that by punishing that person for their bad karma, you actually became the bad person and took their punishment on yourself. The issue is that it can really be argued either way making it too open ended.
Enter natural karma....
This is a similar idea but goes back to basics of what karma really is not just the cultural perception of it. Karma is action. It is the comprehensive collection of all your actions as an impact on yourself and others. A much more natural way of looking at karma is that what I do and what I put out generally will come back to me in some sense. HOWEVER, unlike karmic law it doesn't require that be the case. The major difference in a naturalistic belief is that what happens to you is essentially what you do, so everything that happens is largely a product of your own doing. This is very hard to accept if you've had terrible things happen to you. The way it is explained in Hinduism for example is that if you were God the terrible things that happen to you are quite literally your own doing because you're God and you're just playing the game of life. This seems far fetched to westerners and kind of ridiculous, but this can be understood through breathing exercises. When you practice breathing and focus on it, you are making yourself breathe, being completely aware of your breathes and making yourself inhale and exhale. After sometime of this though you notice that you are now breathing, inhaling and exhaling without having to make yourself do it. It is now happening to you. This is the simplest way to show you that what you do and what happens are much more together than they are separate. Like the Yin and Yang, they are one, but try to appear as separate as possible. This is why largely in Zen, you'll see that meditation and breathing exercises are typically their way of realization and enlightenment because it helps you come to the understanding of what "God" is.
Free will when talking about naturalistic karma can also go both ways. In one sense you can say by taking on full responsibility for everything that happens to you, you have total free will to do as you please and no one else can be blamed for it. On the other hand you can say because only you are to blame for everything, you may feel that anything bad that happens to you from someone else is unfairly attributed to your own doing which you feel you didn't want to happen thus you have no free will at all. The later is more of an argument where as the former is more of a realization. However when you do really think about it, it makes sense to take responsibility for what happens. If I blame luck for not getting a job promotion while the person who got it went the extra mile and was responsible for their own actions to achieve their goals, then it's really my fault, not luck's. I could have easily done the same thing, but left it up to luck so I could give away responsibility. This happens all the time when people ask for advice and then when it doesn't work they just say it was bad advice and move on to seek out other advice givers.
Both versions can be argued, but personally I subscribe to naturalistic karma, though it is more abstract, it holds the most merit in explaining why negative things can happen to good people. Life is not bound by such rigid and strict laws, but rather laws that are defined by us as we understand them.
Why does any of this matter? Well I think naturalistic karma is the most reasonable concept we should all subscribe to. It replaces concepts of luck and anything that allows you to give away responsibility of what happens to you to someone other than yourself. It is a way of taking charge of what is happening in your life and being extremely present and mindful. That is assuming you have free will at all.....
Thoughts?