You've asked three related but not identical questions here which makes it hard to figure out what your real concern is and how to solve it.
- is the safety ground separate from neutral.
- how to identify and distinguish the safety ground from neutral.
- is the voltage between hot and neutral greater than hot and safety ground under load.
The first two questions have a common issue which is whether and where the safety ground is connected to neutral.
I will answer assuming a US installation.
For your first question:
Safety ground and neutral are supposed to be tied together in one and only one location, the main service panel.
Sometimes you see receptacles where the receptacle's neutral and safety ground are both connected to the circuit's neutral because the house was wired without a safety ground. If you are trying to detect this, a visual inspection of the receptacle's wiring is the most reliable method.
Sometimes you see houses with incorrectly wired subpanels. In a subpanel, safety ground and neutral are required to be separated. Visual inspection is the best way to verify this also.
For your 2nd question:
maple_shaft's answer is good with one exception. The problem is he uses the ideal wire model where there is no wire resistance. In fact, 14 gauge wire has a resistance of about 0.25 ohms per 100 feet. Assuming the circuit is wired correctly and safety ground is bonded to neutral only at the main panel, a heavy load like a hair dryer will generate enough voltage drop across neutral from the load to the main panel to be easily measured. I personally verified this ten minutes ago.
For example, 15 amps will generate a voltage drop of 3.75 volts over a 100 foot neutral. If you put your voltmeter between safety ground and neutral at the same receptacle as the load, you will see this 3.75 voltage drop.
For your 3rd question:
Under a heavy load, the voltage between hot and neutral will be LESS than the voltage between hot and the safety ground. In the above example, there will be 3.75 volts less.
Putting my proximity voltage detector within 40cm of the unit resulted in it beeping (it usually needs to be within 1cm to detect anything.)
This usually means hot/neutral is reversed. There might be nothing wrong with the washer. Call an electrician first. And ground that outlet! Your machine's electronics will thank you.
(FWIW I use a non-contact voltage detector daily for diagnosing home appliances.)
Best Answer
Quickest way is to turn off the mains and unscrew the socket and determine the polarity by the colours (Blue being NEUTRAL and brown being LIVE).
Otherwise if you have an EARTH connection nearby (copper pipe for instance) use that to determine which one has the highest RMS voltage from EARTH. Neutral shouldn't be that far off EARTH while LIVE should be 230V (ish)
(this is also why I like the British mains plug)