The software process that develops the applications are very different. An avionics system must be able to operate autonomously, must have robust fault detection and tolerance, and must interact directly with many hardware components.

Web apps tend to layer on top of other systems and can reuse a lot of code. When I worked on avionics software we had to develop everything, from the hardware drivers for memory modules to the drivers for the display and all of the controlling systems for each of them. A high-performance web app just needs to perform well enough - at some point you can add more hardware. In an avionics platform you have specific weight, cooling, and power requirements that limit your total hardware capability. They are really very different.

A good analogy would be the difference between being a brief writer for a law firm and being a fiction author - you have "writing" in common (hopefully "good writing" at that) but the intricacies of each domain make it appreciably different.

Web application programming relies on a plethora of "soft" technologies (xhtml/html5, css, javascript, sql/nosql, php/python/ruby/perl, frameworks for all of it, a lot of 3rd part libraries outside of the frameworks, etc...) - embedded programming is much more low level in comparison and comes with many different kinds of problems.