Mark -
J0anne did a good job explaining the difference between gold and commerce. Commerce is represented by the gold colored coins on the map and from trade routes in your city screen. These gold coins come from cottages, riverside tiles, gold/gem/silver resources and some calendar resources. It's an important concept to understand that commerce is not gold. When you are calling it gold you are confusing yourself and others.
With that said, commerce is converted into beakers, gold, culture and espionage points depending on how you run your sliders. (Basically gold or true income is the result of not running your research slider or combination of other sliders at 100% - it is as simple at that) Of course, the amount of gold generated at lower slider levels is impacted by city/unit maintenance costs) There are many times during rapid expansion early where I was generating negative gold per turn with the research slider at 0% and would have to adjust tiles worked to accommodate this until I recovered my economy.
It is often necessary early, especially at higher levels, to lower your research slider for a while to generate gold to fund your expansion. This is quite normal. It's learning how to manage this properly that is part of the game. Maintenance cost from cities grow over time but can be reduced by certain factors such as the Organized trait, building courthouses in cities more distant to the cap (you don't always need them everywhere, and the Forbidden Palace NW and Versailles Wonder, which I rarely build.
So as an example, say you are running research at 100% and have settled a few cites, so that you are essentially in deficit research (i.e., you are losing a little gold in your bank - say -2 gold per turn). You build a mine on a gem resource and plop a citizen on it to work. This does not instantly translate into gold because what that gem resource is providing is 5 or 6 commerce (not sure of the actually total commerce of that improved resource at the moment. However, because you are running at 100% beakers you just increase your beakers significantly (relatively speaking). Now try this by running your reearch slider at 0% (before and after). In this case, you would see a significant increase in the amount of gold output.
J0anne refers to raw gold. Well, this is basically gold or currency (cash) - whatever you want to call it - it is the money the supports your economy. Lower your research slider generates gold. There is something that I like to refer to as "static" gold, i.e., gold generation per turn that is not impacted by the slider (unchanging, thus, static). The best example of this is the gold generated by holy shrines. For each city that religion spreads to the shrine income increases by 1gpt. Markets, Banks, Grocers and Wall Street multiply this effect, which is why Wall Street is often built in shrine cities. The nice thing about "static" gold generation is that it never changes based on how you run your sliders and therefore the multipliers (markets, etc) are always in effect. Other examples of static gold are corporations and Spiral Minaret effect.
Building wealth on the other hand is a way of producing static gold using hammers. This is a great ploy to use during the game at different points to "fund" certain objectives. You could use it to fund another expansion run, a war, or running your research high to get out a key tech. One important thing to understand about "building" wealth or research is it is totally based on hammers. Secondly, it is NOT impacted by buildings the multiply beakers or gold, so building wealth in cities with markets and grocers is not providing any advantage and often these cities are low on hammers. You can build wealth in any city, but cities with high hammer output like unit pump cities or wonder whore cities nets the best output.
Back to commerce quickly - trade routes are another important source of commerce. As with the commerce coins on the map, there are commerce coins in the top left of your city screens that represent trade routes. Trade routes commerce grows over time based on several factors such as the size of your cites, open borders (foreign trade routes), oversea trade routes, certain techs, and buildings and wonders that increase the number of trade routes or percentage thereof. (The Great Lighthouse and Temple of Artemis, harbors, customs houses) If you have a watery map and lots of coastal cities (or potential), trade route income can be huge and the GLH a priority.