Well, TBH, I don't really consider what you listed as savings, either. Maybe the change jar.
We have different investments and different savings. Things like dd's 529, retirement, taxable investments, a farm that's cash rented... all those are investments for a long time in the future (well, not that long for us, as dh is considering retiring at 65, which will be 10 years from now) and with the farm, we may never sell it to get a lump sum from that, so that's almost like having nothing, because we couldn't "tap" it if we were desperate. Kind of like my brother's baseball card collection... worth something, but not liquid.
We do the medical savings plan, but I don't consider that savings or investment. It's money you're going to spend, anyway... just saving some tax dollars.
Then we do have savings... money that is easily accessible that we can have in our hands in a heartbeat (or thereabouts). We have savings for us for a car, a stove, dd's orthodontia coming up in a few years, a new play structure, annual vacation/visit family abroad, and our basement family room makeover. Most of those are all separate accounts, too. Only the stove fund is where it needs to be to buy a new one. The rest, we are still saving for. Then we have an emergency fund in a MM account, which is about 1 yr. of expenses bare-bones or 6 mos. as we live now. I keep some cash, <$2000. We have another "savings account", but it's in a mutual fund, so inaccessible IMO. Then we also have a couple of savings accounts for dd. One at Vanguard and one in the credit union. These are both UGMAs. We save our coins for dd and that goes into her bank, then on to the credit union account.
We also have the stocked pantry (about 6mos now - more after the garden is put up), toiletries, etc. and we heat with wood mostly. We have enough wood for this coming winter, but haven't had next winter's delivered yet (we don't cut our own). I don't really consider any of those thing to be savings... just being prudent.
I think at least an emergency fund would also be prudent.