First understand commercial design and construction of electric fence controllers for agricultural use are bound by legislative rules that they must meet for safety.
There are rules for battery powered units and others for mains units. 10 kV is the max voltage permitted, ~1/3 of that in an ignition system but a lot more energy excepting for those ignitions used in race and drag cars.
Primarily they are only max voltages and pulse time with energy available being the the buyers choice for the application required and with increased energy available comes increased cost.
A unit I have produces 30+ Joules and cost $1k NZ.
It'll sit me on my arse 1 km from the unit.
Simply they discharge lots of capacitance into the primary of a transformer and the secondary goes to the fence.
Typical mains units pulse 1/sec and IIRC the max pulse time allowed is 3ms.
Yep they can kill things but only if they can't get off the wire. The poor old hedgehog is the most common fatality but only when the wire is close to the ground.
Animals that might get caught or tangled are at serious risk too and care must be taken with regard to the terrain to help minimise risk. Fences across sloping terrain where if wrong footed an animal might fall against the fence need be avoided when planning electric fence layout.
Another NO-NO is the electrification of barbed wire........there have been child fatalities from it.
No real problem measuring the parameters electric fence units can produce with 1000:1 and differential probes.