Income can add to wealth if it is used to invest in assets but isn't wealth in itself.
The
actual income you receive post deductions automatically is
part of your wealth. On-hand, actual income, is an asset whether or not the asset accrues additional income via investment. So, if you get $500 from a week of work after deducting taxes and hide it under your bed, it is an asset and part of your wealth, just like the bed and the house and the car, etc. It might be smarter to put it in the bank or invest it in something but with or without re-investment it remains an asset that is part of a larger concept of wealth. So, if you continue to collect such actual income each week and hide it under your bed for 10 years, accruing $1 million (or whatever) under your bed, that is also part of your wealth. Throwing it in a portfolio is unnecessary for the definition.*
*Of course, one has to look at not only assets but also debts and deductions in order to determine wealth. It is complicated but still, on-hand money is an asset.