To me, there is a difference between being rich and being wealthy. Someone with a high income is rich (regardless of spending). Someone who doesn't spend all of his/her income will eventually become wealthy (regardless of income). Richness is an abundance of something (even if that item is used immediately). Wealth is the accumulation over time of that something (ie not all of it is used).
You may not agree with that definition, but it works fairly well in my world view. Most people don't distinguish between them and that lack of difference causes a lot of fights on Anandtech.
To me, if you make over double the average salary, you are approaching the rich zone. True, there is rich and then there is really rich. Those are different, but I'm talking about rich not REALLY rich. I say, if you make less than $100k, you are not rich. Just over $100k is definately in the transition zone to being rich (varies a bit by location, since someone making $100k in an area with average $200k salaries would not be rich, but most places on earth don't approach that level of average salary). If you make well over $100k, then you are definately rich.
In terms of your link above, a $100k income would put people in the top ~15% in the rich category.
Wealth is quite relative. If you spend little, then a smaller pile of money would be a lot of wealth to you. If you live a jetsetter lifestyle, then that small pile of money is nothing to you. I say you are wealthy if you can retire for life with what you currently have (assuming a reasonable return on investments and that you don't drastically change your lifestyle). For example, if a typical Anandtech poster spent $50k per year (with 3.4% yearly inflation adjustments), and dies in 50 years, he/she would need a pile of at least $1 million dollars (post tax and earning 8% return) to be wealthy.