Web artist is basically and mostly a web designer who visualise and represent his/her idea in the form of unique web experience. Not all web designers are web artists.
Normally when you say web designer it means a person who can design websites and has knowledge of using web design tools/applications, which doesn’t necessarily means that he/she has a proper design sense.
Finding artist in web designer
These days it is very difficult to find web artist in a web designer but its not impossible its only about how you deal with it, the reason is because of too much commercialisation the web designers have to limit their imagination in order to entertain the business requirements and making the stakeholders understand and agree who are all involved in the process.
The shortage of time and money comes together to produce typical website which are ok to go and good looking following the recent trends.
The difference is just like a fine artist vs graphic designer, graphic designer simply works for commercial stuff, he/she is restricted to follow the customer requirements and needs agreement of everyone involved in the process. The fine artist has more room and is not that limited, the fine artist doesn’t necessarily have to make people agree on it and its usually a one person’s direction to achieve the end result and most of the time the end result is not easily understandable for everyone even if the work is amazing.
Simple is for everyone, not art
The reason why people began hiring individual artists instead of giving jobs to companies is because they need unique ideas and designs for their product/brand. Now let me explain you why is this so, making people agree on one idea is very difficult that is why designers usually find a way that is by making things simple that everyone can understand, which is good and this has been proven by top of the line brands like Apple which produced simple and easy to use interfaces because it easily understandable for masses and that has become a unique selling proposition for some of the successful companies. Google is also following the simplicity in their new material design and so as the other companies.
Individual direction and crowd contributed direction
Now as far as web designers are concerned, they could be web artists as well. It depends on the people/clients he/she is dealing with. If the clients are that flexible and give more space to web designer the end results are usually amazing, to prove this you can compare WordPress themes with professional websites, ever wondered why WordPress themes are better designed in experience? It is because those are usually coming from individual web artist working on one direction and execute the product in much unique and polished way. Its not even only about individuals even sometimes the teams are flexible enough to give more space and room to designers to execute the project in their direction.
An experienced web designer has a proper sense of dealing with customer requirements and knows how to represent in design. Its the designers decision after knowing the client to design it in artists way or commercial way.