I found an eBay listing for a US 70w M85 F-Can ballast made by Advance. As I looked at it, the ballast says that it is NOT compatible for single ended MH lamps. I do not get it. Can somebody explain why MH ballasts for double ended MH lamps are not compatible with single ended MH lamps or is the ballast just a relabeled M98 ballast?

Here is the eBay listing for this ballast:

https://www.ebay.com/itm/263829275177

This is BS. M85 ballast can run most 70W MH lamps that are compatible with European 70W HPS/MH ballasts.
As American E26 70W pulse-start MH lamps, can work on European 70W HPS/MH ballasts without problems, I don't see any reason for the state that this ballast would be suitable for double ended MH lamps only.

Double ended lamps are rated for higher ignitor output voltages, as used in fast hot restrike gear. This makes sense, as there is no small Glass/Quartz insulation bit (the Vitrite isolator in a screw cap, or the Quartz between the 2 pins in a compact lamp) subjected to high voltage gradient. (It would probably not do anything in ideal conditions, but if the Vitrite is dirty and maybe a little cracked too, it could arc over and then start burning up resistively)

I dont see the ignitor output voltage stated anywhere on the ballast, allthough it does not seem to be any special fast restrike ballast - so its ignition voltage probably doesn't exceed 4.5kV, and could be down to the 2.5kV range ? - In this case there wouldn't be any problem with running any type of lamp

In some other ballast configurations this could have been also related to the lamp screw shell not being tied to Neutral, however in this ballast it is, so that's not the reason

In the wiring diagram, I see none of the lamp wires connected to the common Neutral.
To me it looks like both wires going to the lamp are live, at least during ignitor pulsing.
So first by this technique you may get 8kV across the lamp while still have only 4kV towards ground, so you get faster festrike while still do not wxceed rating of the lamp contacts. But when connecting standard screw base, there will be the full 8kV in very close proximity.

Second problem is electrical safety and an impossibility to wire it in a code compliant way: Canada, (as well as many company rules) does not allow the shell to be on any other potential than Neutral or Ground (or have the construction so it is covered from touching once it is connected - only used in Europe and only for the mains voltage, not for connection with HV pulses on it). This means when this ballast has both wires live (perfectly OK for a socket style which does not have any conductive shell contact or has no screw shell at all), there is no way to wire it in a compliant manner to any screw in base socket.

Ok, so does that mean that running a DE lamp of 70 watts on a M98 ballast will work satisfactorily but with longer restrike times ?

...you may get 8kV across the lamp while still have only 4kV towards ground, so you get faster festrike while still do not wxceed rating of the lamp contacts.

Is the 4kV rating of a typical ceramic socket across the terminals, or from terminals to ground? I understand the concept of center-tapping to reduce voltage to ground, If there is no ground nearby, how is ground a relevant frame of reference for the socket?

I expect that the ignitor voltage is clamped by the lamp discharge fairly immediately if the lamp strikes normally. But if the lamp is too hot to be able to restrike, or is leaked or not present etc, the voltage all components get is the full ignitor output. If a component can't handle this voltage, it will fail

So, using a fast restrike ignitor on a lamp that can't handle it, will not affect the lamp restrike time or normal operation, but make more significant risk of damage to the lamp or other luminaire components during a hot restrike event

The components in a luminaire that are subjected to voltage towards Earth are wiring to the socket, socket itself, and any connections. The socket is also somehow mounted to the luminaire, most commonly with screws. In most modern sockets the screw heads are inside the socket, and the screws and bracket they attach to go in the socket base near the terminals. (The double ended lamp holders also have metal brackets that hold them, so they are not exempt from this either)

A clean ceramic socket would hold voltages way above 4kV, whether between terminals or to ground. But you gotta account that sockets can work in dirty, humid, etc environments that lower the voltages at which problems start, so take big spares on the design to prevent the problems from becoing commonplace, or pose a safety risk, etc

Any surface which is not very clean or is moist, is susceptible to arcing over, even at line voltage (not necessarily ignitor output voltage). Some materials like Plastic and Glass can become conductive after the first arcing, so keep burning up from resistive heating of the decomposed material (Plastic that decomposes to Carbon, or Glass that is naturally conductive when melted)

The schematic on the ballast in this case clearly shows that the lamp is connected with one end to Neutral, so the voltage to Earth or across the lamp would be the same

Is the 4kV rating of a typical ceramic socket across the terminals, or from terminals to ground? I understand the concept of center-tapping to reduce voltage to ground, If there is no ground nearby, how is ground a relevant frame of reference for the socket?

It is between any two conductors that happen to be close by. So with screw sockets you have all 3 there: L is close to N, as well as both being close to the earth. So there is no way to feed the lamp anything above the rated voltage without exceeding the socket rating. Now the rating could be asymetrical, with some contacts having higher than others, like for HID pulse ignition, these sockets are rated to see the high voltage pulse only on the center terminal.

On the other hand with double ended sockets you have only one wire on each end, so that wire is only close to the ground and has practically no relation to the other contact being 12cm away. So if you use the "center tapping" concept, you may rwach double the voltage across the lamp compare to the socket rating, as this socket limits the voltsge only between a live wire vs ground.

Now whetger this ballast uses center tapping or not, you have to check yourselg. I see it only as low resolution image (can not read any text on wire or connection labels, just assuming from how it is drawn), got an impression from it the Neutral is not connected to the lamp, but I could be wrong on this. So check that yourself.