It's just the one 4-economy cycle and the other 3-economy I described:
Mining -> Manufacturing -> High Tech -> Power Generation -> Mining
Trading -> Processing -> Research -> Trading
The descriptions that fall into each are kinda straightforward once you know that there are only 7 types but a couple were confused at first to me (e.g. I incorrectly guessed Ore Processing comes after Ore Extraction but it doesn't).
It does show in-game if you 'Discover' a planet and check its Discovery menu entry, or if you look at the planet description on a trade terminal -- it will show an icon that represents 1 of the 7 Trade Types.
Then, every Trade Item in highlighted texted says which Economy type it's meant for -- that's where I got the 7 titles for the Economy types, BTW (e.g. I didn't just think personally think Mining summarized the 4 descriptions -- Trade Items from the 'Pickaxe icon' Economy type are called Mining Trade Items; same for High-Tech, Manufacturing, etc).
That said, that's a bit slow because you basically need to physically travel to every type and keep track
Basically it's the following:
Economy Trade Cycle: Mining -> Manufacturing -> High Tech -> Power Generation -> Mining
Mining -> sells to Manufacturing
Icon: pickaxe
Planetary economy descriptions = Mining, Ore Extraction, Minerals, Prospecting
Manufacturing -> sells to: High Tech
Icon: gears
Planetary economy descriptions: Manufacturing, Mass Production, Industrial, Construction
High-Tech -> sells to: Power Generation
Icon: microchip
Planetary economy descriptions: High-Tech, Technology, Nano-Construction, Engineering
Power Generation -> sells to: Mining
Icon: battery
Planetary economy descriptions: Power Generation, Fuel Generation, Energy Supply, High Voltage
Complete cycle:
-->> Mining, Ore Extraction, Minerals, Prospecting -->> Manufacturing, Mass Production, Industrial, Construction -->> High-Tech, Technology, Nano-Construction, Engineering -->> Power Generation, Fuel Generation, Energy Supply, High Voltage -->> Mining, Ore Extraction, Minerals, Prospecting -->>
Economy Trade Cycle:Trading -> Processing -> Research -> Trading
Trading -> sells to: Processing
Icon: pocketwatch
Planetary economy descriptions: Trading, Shipping, Mercantile, Commercial
Processing -> sells to: Research
Icon: flask
Planetary economy descriptions: Ore Processing, Metal Processing, Material Fusion, Alchemy
Research -> sells to: Trading
Icon: DNA
Planetary economy descriptions: Research, Science, Experimental, Mathematical
Complete cycle:
-->>Trading, Shipping, Mercantile, Commercial -->> Ore Processing, Metal Processing, Material Fusion, Alchemy-->>Research, Science, Experimental, Mathematical -->> Trading, Shipping, Mercantile, Commercial -->>
I think that's all the descriptions but as a disclaimer I've spent probably 90% of my time doing the Mining cycle so there could be descriptions I've missed.
I mentioned that Wealth Levels are the same but I think they're even more straightforward, but a few examples I quickly remember:
Wealth Level Types: Descriptions
Rich: Wealthy, Affluent, Booming
Medium: Moderate, Satisfactory, Stable, Sustainable, Medium Supply
Poor: Failing, Low Supply, Destitute, Developing, Fledgling
There's quite a few but I think it's generally easy to tell which is which. You can also manually notice the different Wealth Levels by comparing the prices of items in each manually, or more easily just use an Economy Scanner and you can notice each has a range of percentage change (above/below Galactic Average) that I described in the main post earlier.