The actual sequence of events may vary depending on server OS, number of CPUs, (number of servers if using a load balancer), type of web server and PHP installation, and so forth.
Generally speaking, each request will run in its own process and memory space and won't care about any other requests. (While an individual PHP script may not be able to multi-thread, that does not mean the web server cannot spawn multiple, independent PHP processes.) Probably the only times they will have any sort of conflicts will be when hitting the database or during file I/O, and that's usually not an issue unless they are both trying to write to the same DB row or the same file. A DBMS usually handles simple cases of this just fine without you having to worry about it, though in more complex situations you may need to implement some DB transaction processing with table/row locking. (I think I've used transactions once in the past year, and don't remember when I last did any explicit DB table locking. I think I had to implement some file-locking once in the past year or 2, as well.)