For the first method,Coming from stackoverflow, You can literally just install php and run it from the command line. For someone who is experienced with computers and technology, and the use of their command line, this is probably the easiest way to go about this. The downside, however, is that not everyone is so knowledgable. A simpler method and a more structured one may be preferable.
Asynchronous Multitasking PHP, or AMPs, appear to be a way of reducing the complexity of the first mentioned method, by adding in a special blend of libraries and packages that would make the code more structured, while still keeping it local. It appears you're able to access other server programs and use them, like MySQL. While this still may be complicated for some, writing the code becomes much easier thanks to the way that AMPs are set up.
AMPPS appears to be a specialized AMP, and appears to be the most user friendly. They have an auto-installer that adds in a boatload of helpful managers for PHP, Wordpress, Apache, MYSQL, MongoDB, and hundreds of apps on top of that. alongside being able to backup your content, ampps seems to style itself as being the most helpful. There is of course one caveat. That you have to pay for detailed versions. While there is a free version, it does not come with all the bells and whistles, and the second cheapest variant starts at $49 per year.
In Summary, We looked through 3 various ways to run PHP locally. The first way is just simply installing php and running it through the shell. The second way is to use AMPHP, a method that uses many libraries to structure the code. The third way is effectively a direct upgrade to the second way, however comes at a steep price, but is the most powerful way nonetheless.