A great question
Welcome to Code electrical. You're starting off with a very astute observation and a valid concern. It's about the difference between an isolated system and a grounded system.
Power doesn't want to go to ground. It wants to return to source.
Chevy Volt - 2 systems at once
Automobiles have an apocryphal "grounded system". It's a 12V electrical system with ground (i.e. chassis) pegged to an arbitrary location in the supply power, almost always negative ground by convention. Positive ground does exist. (chassis is also used as a current return; that's a separate issue.)
The Prius or Chevy Volt also has a high-voltage traction electrical system - batteries, electronic inverters, motors etc. which is fully isolated from the chassis of the car. Any leakage from the high-voltage system is considered a fault, even from the "negative" side, since "negative ground" is not a concept in an isolated system.
Enter the world of Code electrical, which applies to structures. There is a religious battle between isolated systems and grounded systems, with grounded systems winning.
Industry sometimes uses isolated systems. I have a 480V 3-phase system, all three phases isolated from ground. If one phase faults to ground, it's an unintended ground strap, and the system is no longer isolated. If another phase faults to ground, kaboom! It takes two failures to have a problem, and the idea is frequent inspection catches the first one. It's a fine philosophy. If your accidental contact is the first fault, you only get hit with biasing current, and hopefully death "gives you a mulligan" (second chance).
Household electrical started out "isolated" because grounds were not a thing. They went with a grounded system where you intentionally peg the system to ground rather than waiting for a "first fault". Only one more failure creates a problem! Downside, no mulligans like in the isolated system. Upside, most faults cause an immediate and big problem, which assures a circuit breaker trip.
Power doesn't want to go to ground. It wants to return to source. By bonding ground to a conductor, now power wants to go to ground too.
Which is better? Like most of the Electrical Code, it's not about ideology, it's a numbers game based on a lot of accident reports.
Ground can be pegged ANYWHERE
Different systems see it different ways.
- Euro power is 230V with "neutral" being at one extreme.
- UK construction sites are 110V transformers with center-tap grounded. The tool sees 110V and there's a safer 55V from any wire to ground. Interestingly, this system does not have a neutral.
- North America is the same, but 240V, and the center tap is brought out as neutral, allowing 120V circuits.
In principle you could peg ground somewhere else. Like the UK tool system where ground is tapped where no conductor is, you could design a 6 volt AC bias between neutral and ground. Or with a 6 volt DC bias. Look up "wild leg delta" for a truly screwball ground bias. My point is, it's arbitrary and there's no Godly answer. There are merely agreed conventions and codes (some of which are rather clever, like wild-leg).
Neutral Is Not Ground
This is the hardest thing for a newbie to understand when he's staring at the panel and seeing a tangle of copper and white going to obviously the same place. What you're seeing is an ugly shortcut, and I'll explain that soon. They have wildly different purposes.
Neutral is the current return. It is a conductor which normally carries current.
Ground is a safety shield. Current should never flow through ground; if it does, it's a ground fault.
If you can put a clamp ammeter on the neutral-ground strap, you should see 0.00000 amps of flow. In fact, that's a pretty good system test.
Where to bond neutral and ground
Remember the isolated system, where the first ground fault was only a bias, and it took 2 ground faults to cause trouble? Your ground-neutral bond is the first fault done intentionally. Think it through -- that means there should not be a second. Neutral and ground should be bonded in only one single place. The single place is the main panel.
If it was bonded in 2 places, current tries to flow down all available paths at once. The ground path would end up seeing some of the return current intended for neutral, and that's not its job. Worse, what if there as a neutral wire break between those two points? Current return would detour down the ground wire. Again not its job, and ground wires are allowed by code to be thinner than neutrals in some cases. It would overheat.
A perfect panel
In an ideal panel, there is a neutral bus (insulated from the steel panel), a ground bus (attached to the steel panel), and all the neutrals go to the neutral bus, and all the grounds go to the ground bus.
If this panel is also a main panel, there is one, single, neutral-ground bond tying the buses, and in a dream world, enough space to clamp an ammeter under it.
Real world, most homes have only a main panel, so practical electricians just slobber all the neutrals and all the grounds onto one bus and call it done. When you see that, that's all you're seeing. I hope I don't give you an OCD attack.
What's a benefit of doing it "ideally"? You have several options for testing the ground-neutral relationship. You're in a good position to replace your main breaker with a "whole panel" GFCI. And if you upgrade service, you can add a new main panel, and convert this to a sub-panel just by pulling the bond. Which means not having to rewire the whole panel.
Yes, the conductors have electricity flowing through them. Yes, normally you should respect and fear any conductor.
However, by design, this is a grounded system which intentionally pegs the neutral to ground at the panel. Since current flows on neutral, voltage drop occurs (E=IR) on neutral, which means neutral won't be the same as ground everywhere, but it should be close, by design. So, ground and neutral shouldn't bite you unless you're touching hot.
You have the right idea, install an indoor-rated GFCI outlet near the panel, and then use the LOAD terminals to feed a second receptacle outside.
By the way, many panels have an "electrician's outlet" a few inches away from the panel. This is so the electrician can plug in lights and tools while he wires the panel. This is typically on its own breaker if there's room.