The Swedish tax system allow both models and it up to the stock owner which type they choose (chosen when creating the "stock account" at the bank). You either pay income tax when a stock is sold, or you pay the same income tax on the value of the stocks based on a fixed predetermined estimate on how much stocks is expected to increase in value (based on the rate for the government debt and then added 1%).

Each model has benefits and drawbacks for both the government and the tax paying citizen, and both works. Taxing wealth directly has the benefit that it gives the government a more even and predictable taxation each year, and the citizen benefit by gaining any additional profits that is above the rate for the government debt+1%. The downside is that the government may not get as much tax as it could as the yearly stock value increase tend to be a bit above that predetermined value, and citizens may loose out a bit more when there is a significant crash.

The benefit of taxing only when people sell stocks is that the government get the whole income tax, and the citizen do not have to pay any tax if they don't have any profits. However it seems that most people are going with option 1 since people tend to expect that stocks will go up in value when they invest in stocks. Currently, that predetermined tax is (0.51+1)*0.3 or 0.453% per year of the total stock value.

California is not proposing the "Swedish" system.

Correct, but what I am describing is a wealth tax system that goes after unrealized capital gains from stocks that does not depend on the stock being sold. It can tax the expected value increase rather than the actually value derived when a stock is sold, demonstrating a working method to tax the value of stock ownership rather than at the point of sales. It also demonstrate that people will volunteer to such system if it gives a statistically economic benefit to do so.

If they are taxing unrealized gains in one year, are they returning funds at the same rate on unrealized losses in the next year? (This isn't a rhetorical question. I'm genuinely curious.) I don't understand how this is going to work.

No, a predetermined rate is predetermined regardless if the outcome at the end is a loss or profit.

The benefit of doing so for the investor is that the potential for profits is higher, and on average the predetermined tax rate is a bit lower than the actually tax you would pay after selling the stocks.

Let say as an example you bought stocks in an index fond between 2010 and 2018. The average result from all index fonds was +8%. With regular income tax on sales the resulting profits people got after tax was 5.6% each year. With the predetermined tax they got to keep 7.547% out of those 8%.

But this year the crash might have resulted in less than 0.457% profits, in which case the predetermined tax can be higher than what the income tax would be on sales.