Neutral is completely separate from equipment safety ground. I know your eyeball is staring at evidence to the contrary, but let me describe the system design.
The purpose of neutral is the normal current return. The purpose of Safety Ground is to be a containment shield to contain any electricity leakage.
Isolated systems have a flaw
AC power is wired as an isolated system. The hot and neutral conductors are supposed to stay in their pathways and not touch anything or anyone else. So there should be 120V between hot and neutral, and 240V between hot and hot, and nothin to anything else. I've wired isolated systems, and they have a flaw.
Nothing keeps the isolated system from floating up at hundreds or thousands of volts higher than it should be ... say, because of a transformer leak or a ground fault. Thousands of volts would breakdown the insulation inside appliances. It couldn't hold against that.
Bonding the system
So, to keep system voltages at a sane level relative to outside the system, they use equipotential bonding - between one of the conductors and earth. On a 480V 3-phase delta system, that can be a set of transformers that puts ground in the middle. But on a split-phase system, they simply pick the middle conductor and and make it equal to earth. This type of bond is much simpler; it's just a copper strap. Hey, cost savings!
The conductor bonded to earth is called "Neutral". Ideally, it's near the voltage of safety ground. The safety ground wire is, of course, bonded to earth.
An ideally built panel has two separate bars, one for ground, one for neutral. The neutral-ground equipotential bond is a separate section of wire, and you can get a "clamp meter" around it which is useful for diagnosing problems.
However, house builders are cheap. They pushed back on NFPA (the rules authority) and said "Why do we need 2 separate bars and a bond? Since we're inside the panel, why not just put em all on the same bar, and let the bar be the bond?" Due to their political pressure that was allowed. It's not how I wire panels though.
That's why you're seeing what you're seeing. Recognize it for what it is: legal but lazy work.
There can be only one
The equipotential bond is older than the idea of running safety grounds to every outlet. And it creates a potential (heh) problem: If neutral and ground are connected anywhere else, then they end up sharing the normal current that is on neutral. That means neutral current is running around on the ground wire. If the neutral has trouble returning current to the panel, the neutral wire WILL energize at line voltage. (and this is why the neutral wire has insulation!) If you've tied that to ground also, that means all your grounds are now energized - what should be safe is now lethal.
Often the ground wire is smaller since it never handles current except during a ground fault. Another failure point is if the neutral wire breaks but the ground does not. If they are tied in two places, neutral current can simply take a detour on the thinner ground wire - overheat and start a fire.
Because of both these problems, the firm rule is "There can be only one neutral-ground bond".
And you're looking at it!
A useful side-effect: Containing wayward current
The whole reason we bring safety ground out to points of use is to be a shield to protect from wayward current. The idea is that if electricity goes somewhere it should not, it will encounter a grounded shield before it encounters a human. The ground will neutralize the current - literally. This is where the neutral-ground bond does double duty. Fault current flows back the ground wire, to the panel, through the neutral-ground equipotential bond, and back to neutral.
Electricity doesn't want to return to earth. It wants to return to source: e.g. the supply transformer up on the pole. The bond means that electricity will be happy to return to ground instead of neutral.
So if a lot of current flows this way, hot to ground via the bond back to the transformer -- the high current will trip the circuit breaker. This the ground averts a dangerous shock or fire situation into a quick circuit breaker trip.
Why not just have neutral be the safety shield? It's already there.
Well you're in luck: exactly that is done in pre-1989 homes with dryers and ranges using 3-prong connections. They get 2 hots and a neutral, and no safety ground. The appliance industry didn't want to lose sales in older homes, so they pressured NFPA to authorize attaching the machine's chassis to the neutral wire. What could go wrong? The logic is these appliances are rarely unplugged or disturbed, so they are unlikely to have a problem.
Well, they do. It sometimes happens that the neutral wire breaks. When you open the oven door, the light is wired between hot L1 and neutral. So the light connects L1 and neutral through its bulb (basically a resistor). Except neutral isn't connected to anything else, so what does its voltage become? That's right. 120V. And the chassis is connected to neutral. So what is the chassis energized at? Yup, 120V. You touch the range and sink, or the dryer and the (properly grounded) washer, and kablammo.
And yeah, this has a body count. But it's hard to find it in reports, because it's widely misreported as miswired dryer, when in fact it is correctly wired, but had an ordinary wire break.
A simple wire break shouldn't create a hazard. That's a core philosophy of how the system is designed. Everybody knows the 3-wire exception is an ugly bootlegged hack, but the appliance industry is too powerful to fight.
But let's review from a modern perspective
We know grounding to neutral is bad. But what if we just stop grounding altogether?
After all, these days, we have GFCI devices to protect shock, and AFCI devices to catch wiring faults. Is safety ground even really relevant anymore? Can we just go back to wiring 2-wire like we used to?
That's actually a pretty good argument.
But ground does a couple things for us still. First, it helps arc-fault and ground-fault breakers work better, by giving electricity somewhere obvious to arc/ground to. With a grounded appliance, the fault trips immediately, instead of "lying in wait" waiting for someone to touch it. And second, ground is still instrumental for returning natural electricity - static electricity (ESD), lightning, or for that matter spikes/surges. When you see homes trying to work without grounding, they have a lot higher failure rate in computers, electronics and telecomm equipment.
So ground has its place, and that requires it to be totally separate from neutral (except in the main service panel, the one and only place it bonds to neutral).