What is the difference between an application software and an operating system?

Short answer, is application software doesn't talk to hardware directly but through operating system.

If we want more detailed answer, Operating System or Software is what gives commands to hardware like - memory, hard disk, user input devices etc. For each operating system hardware manufacturers make drivers to be able to use them more effectively. Other than that Operating Software give end user basic functionality like create folders, files, configure devices etc. Most popular Operating systems are Windows, Unix, macOS, iOS, Android etc. Also modern Operating Systems comes with plenty of built in applications.

Application is a program that is generally built for certain operating system where application developers don't know which exact hardware will run their software - all hardware calls is managed by operating system. Sometimes there is intermediary applications like JVM (java virtual machine) that enables same application run in different operating systems.

There is third kind of software - called embedded software - which doesn't need operating system to run, for example microcontrollers like Arduino is programmed just using C language with help of arduino libraries.