It looks to me that in the perception of many distance skaters the phrases "alternating the legs", "switch pushing" and "skogging" have no difference to their meaning and are often understood to describe one and the same thing. But from my undestanding about what the term skogging stands for and from my own experiences with using both legs for pushing I will try to explain the differences I can see.
Although "alternating both legs" and "switch pushing" can be used to describe skogging, they are not necessarily synonymous to the full meaning of it. If you look at the definition of skogging given by Chris Yandall, the inventor of this skateboarding style, it's basic characteristic is: Trying to be pedidextrous. Pedidexterity means being able to use both of your feet to perform a task in an equal way, just like ambidextrous people are adapted to using both of their hands in the same way to do something like writing for example.
If we take this definition, we can see that everyone of us already has experiences about being pedidextrous: Every time we walk or run we have to use both of our legs alternately. And when doing this we perform our strides in an equal way with both sides of our body. Although people usually have a weeker and a stronger side, this does not show when using the legs under normal circumstances. So I call this a pedidextrous skill, through which it becomes possible for us to move forward efficiently. In my view this principle of using the legs in an equal way should be the basic requirement for skogging, too. After all it is jogging with your skateboard.
Even when standing on the board with the feet pointing straight forward our body will still be slightly turned to one side in the hip area. On the image above this is indicated by the elipse. This way the starting position for pushing is different for each leg. The result is that every time we push each leg is used and trained in a slightly different way.
For ChiPushing I like to use a basic foot position like shown on the image above. The front foot is pointing straight forward while the back foot is placed with the toes pointing slightly to the side. This way your stance on the board is more firm and secure during higher speed. As a result the hips and torso will be turned even more to one side. Because of this it is even more important to switch between goofy and regular stance instead of just pushing mongo, if you want to train both legs in an equal way.
Alternating both legs for pushing
Some Skaters are using both legs for pushing, but not in a purely pedidextrous way. They are only alternating between pushing regular and mongo or goofy and mongo. But this means that they are keeping their original stance (either goofy or regular) and when using the other leg they just take their front foot off to push on the opposite side of the board. There's no doubt that using both legs this way can be efficient to push on longer distances and it already takes a good amount of practice and balance to use your front foot with the same effectiveness you are using your back foot. But while doing so you are still not changing your original stance. If you are goofy, you stay goofy and if you are regular, you stay regular. The only difference is, that you are alternating between using your back foot and your front foot for pushing. Of course this can be a good way to start learning to be pedidextrous, but this method itself is not pedidextrous in the real sense of the word.
Even if you stand on your board facing straight forward, like a lot of distance skaters do, your body will still be turned a bit more to one side in your hip area. This way you are not using both sides of the body in a completely identical way. You will feel this if you exchange the placement of your feet on the board by putting the back foot to the front and the front foot to the back. Even if you are well trained in using both legs with this method, after the exchange you will still not be able to push with the same effectiveness than before. The reason is that you have failed to train your body to adapt itself to pushing mongo with the other foot. This is a sign that you have not yet completely mastered pedidexterity.
Of course mongo pushing can be a part of skogging, as you can see in the videos of Chris Yandall and Steven Meketa on YouTube. But it is wrong to think that you are already skogging when actually limiting yourself to only pushing mongo on one side. This can only be a beginning or supplementary skill of skogging. There is still much more to accomplish when using both legs alternately.
Some skaters are switching sides only after pushing for longer periods has tired their muscles in one leg. The good thing is: They are changing their stance between goofy and regular. But if they are only doing it occasionally to relieve their main pushing leg for some time, they will probably never really develop the same power and skill in both of their legs. Although switching sides from time to time, they will still continue to train their body in an unbalanced way. Although they are indeed pushing switch, they will continue to favour one side over the other. When skating switch they will always be aware that they are skating "switch" and not in the stance that feels more comfortable to them. That's why in certain situations when speed or acceleration is required they will always use their strong side. This again is a sign that they have not completely mastered pedidexterity. To think that you are skogging just because you are able to push on your other leg for a while is also wrong, as you still haven't found fun in the frequent transition between your two legs.
ChiPushing and Skogging
If you have trained yourself to be really pedidextrous, the change from one stance to the other will be naturally and easy, as you have freed yourself from the restrictions of being goofy or regular. In this state you are truly skating in a stanceless way without any preference for one side. Only then Skateboarding will be a truly balanced workout for your body and your body will be truly prepared to achieve the best possible results when skating long distances. To me this is what really can be called skogging. The practice of ChiPushing can help you to reach this state of stanceless distance skateboarding more easily: Through the relaxation of your body and the dissolution of obstructions to the flow of Chi in your joints, together with the right body posture and the knowledge to move as a unit when pushing you will develop a deeper physical sensing, which will allow you to move freely and with improved balance. In this state the switch to the other leg will happen easily.
I don't want to criticize anyone. Actually I think, everyone who is changing their legs for pushing is great, no matter how they are doing it. They all have my appreciation because everyone of them has made the right decission to use both legs for pushing. This helps to spread the awareness about pedidexterity in skateboarding which also helps to spread the awareness about skogging. The real purpose of this text is to remind us all that skogging is not something simple that can be done easily. Let us never stop progressing our skogging-skills through constant practice, because there is still so much more potential hidden in the art of pedidextrous skateboarding.