Every problem has its own unique requirements. If there is no existing solution to the problem, you have to make one. That’s design. You look at what the thing needs to do, and use your imagination and experience to visualise something that satisfy your requirements.
A design is said to be good when it achieves the result it is designed to deliver. The result you aim to achieve may be purely functional, measurable with hard data, or it may be an experience, which it’s less easy to measure.
Web design is the creation of a new solution to a problem in the web medium. It includes graphic design, because the output will be consumed through a visual medium.
But it goes further than the purely visual. It stretches to incorporate every aspect of a web experience.
Designing a web experience may incorporate some or all of the following list of disciplines. Some come under graphic design, others are broader design.
For a web site to live up to its potential, it must attract the right audience, and in the right numbers. That means it must be optimised to be found for people searching for what the site offers, whether they find the site via organic (i.e. non-paid) search, through advertising, social media, or PR.
A successful web site must also sell. Every site has a purpose, which should be to generate action by the visitor. A website that sells is one that generates that action, whether it is to buy, to sign up, or just to read.
Graphic design is the creation of new solutions to problems within the medium of visual communication, either in 2D or 3D, on paper or digitally. The output is usually something that can be reproduced in order to deliver its objective many times.
The outcome of Graphic design includes logos, web site user interfaces, tattoos, sketches for fashion or industrial design, typefaces, print, animated characters, advertisements, flyers, movie credits, newspaper headlines, and designs for textiles. This is just a small part of what can be designed graphically. What they have in common is output that will be consumed through visual media.