>Yeah, that's how insurance works: it is wealth distribution from those who have not become (yet) an insurance case to those who have not.

In the context of differentiating between wealth redistribution and insurance, insurance does not redistribute wealth, insurance redistributes risk since underwriting in a competitive marketplace ensures you only a premium commensurate to your risks.

For example, the government mandates only liability insurance up to $x, for which the premium for the same coverage can be vastly different depending on each person's driving history. While this can be considered a tax because the government mandates it, one can see how this is not wealth redistribution since the "tax" being paid is at least partly dependent on one's risk profile.

Contrast this with a government mandated defined benefit pension contribution equal to a percentage of one's earned income, with a known fact that one's contributions will reflect their benefit less and less as the years go on. That is far more "wealth redistribution" than "insurance".

Another example is in the US, health insurance premiums are more tax than an actuarially calculated premium based on health risk. This is because health insurers are not allowed to price health insurance based on health risks. It is explicitly a redistribution of wealth from the young and healthy to the old and sick, due to the maximum age rating factor and inability to underwrite based on pre-existing health conditions.