Insurances are not hedges. Hedges are „investment position[s] intended to offset potential losses or gains that may be incurred by a companion investment“ (wikipedia) of which insurances can be a part of, while in an insurance „a party agrees to compensate another party in the event of a certain loss, damage, or injury“ (wikipedia).
Absolutely not the same thing. But even so there is still an interesting insight to be gained from common parlance:
Usually we talk of a bet in a situation where you take an event that is somewhat out of your control and irrelevant for your wellbeing and intentionally and actively make some kind of material outcome for yourself depend on it. In so far speculation at stock markets is „gambly“, you are right about that. And if you have measures in place that hedge the risks of those speculations you might be tempted to very loosely call those your insurance.
If you look however at how the term insurance is typically used you can see a difference there: you insure against risks that are non-avoidable risks of your daily life or business. You do not intentionally and actively enter the cancer-lottery. And you do not actively take measures to win your „health-insurance-bet“ because the outcome is still considered catastrophic, even in case of „winning“ it.
And the way people tend to see things more as insurance vs. bets follows exactly these lines: is it about mitigating a devastating natural risk that is hard or impossible to avoid 100% or is it about something where you actively and intentionally attach your wellbeing to a random event. (We could separate this out in two questions: do you involve yourself actively and intentionally; and: is the outcome that you bet on inherently against your intrinsic interests. But that is a detail that I don‘t think we need to go into)
I think this explains the common parlance quite well: health-insurance: the risk is unavoidable, you do not willfully enter some kind of cancer-lottery on whose outcome you bet. Also you have an intrinsic interest in not „winning“ said „cancer-lottery“. -> no doubt it is insurance.
Legal expenses insurance: risks depend largely on your behaviour but you usually still have an intrinsic interest not having to use it. -> some people might see this as more gambling- or “bet-“ adjacent.
Speculating on one stock and hedging that bet. -> Totally not an insurance. Also not something insurances do. An insurance might be part of your hedge (maybe insurance of freight against loss) but insurers typically do not insure bets. Which makes sense, since part of their business-model is that the customer has an intrinsic interest that the payout case does not occur.