Disclaimer: After I have met with the world espresso champion who is also a local coffee producer in El Salvador today, I decided to improve this answer.
I think, one should know the diversity of these three main techniques to distinguish the differences. There will be other minor techniques, as well.
All these techniques are in essence used to protect the bean from bacteria, mold and fungi right after the harvest. The coffee fruit is full of sugar and fermentation starts rapidly after the fruit leaves the tree. Thus, peeling of the fruit from the bean rapidly may help to get rid of the mold risk. If you choose to get the fruity tastes affect your bean and leave the fruit around your bean, then you should take proper care about mold and fungi. This may be especially difficult in big plantations as you need around 20 days and huge flat areas.
Wet process can be said the industry standard. The fruit is totally peeled off to the bean, then the beans are dried.
1.a. Double-washed process is a process that the fruits are first washed to the bean. After the fermentation starts, it is washed for a second (or several) times. This technique is also known as Kenyan process. The result is a very clean flavor.
In dry process, the fruits are left intact to dry themselves. During this process, they should be moved regularly to protect them from mold and fungus. When the humidity is around 13%, they are peeled of, washed and dried for the second round.
In Semi-dry/semi-washed/pulped-natural/honey, just the skin of the fruit is peeled of, but the meaty part is left on the bean. Then, the fruit is dried, peeled of to the bean, washed and dried for the second round.
3.a. In 50% washed processing method is the method where the processing is akin to honey method, but the meaty part of the fruit is peeled of halfway to the bean. This peeling of may be done in the beginning or sometime during the fermentation. As mentioned, the aim is balancing the sugar level and protecting the beans from mold, etc.
It is clear that pulp-natural or dry processing are costlier than wet processing -whatever the metric is; monetary, labor or time.
Another factor is flavor. Dry or pulp-natural processed beans include more fruity notes as the fruit fermented together with the bean during the first drying phase.
(It is said that pulp-natural beans are less acidic than dry beans, but I have not experience that myself.)
Note that, dry or pulp-natural processing is not available everywhere. E.g. if you see a bag of Guatemala dry processed beans*, just run away. As Guatemalan weather is so humid, you can hardly dry process the fruit without mold.
(*) Probably, it doesn't even exist.
Further reading that matches origins and processing techniques.