IOR: is any method of producing or injecting (developing) a well (reservoir) that is not on primary production or commingled (not selective) production such as (secondary recovery like water flooding and tertiary like gas injection, chemical injection or microbial injection.

EOR: its tertiary recovery techniques for increasing the amount of crude oil that can be extracted from an oil field either by using Gas injection, Chemical injection, Microbial injection or Thermal methods.

I do not think that there is any difference. Petroleum engineers normally inject water into an oil reservoir to maintain the reservoir pressure (and hence the ability of the reservoir to pump oil to the surface). In the process and if the water injection wells are properly located, the injected water normally sweeps (pushes out) out more oil effectively flooding the reservoir and increasing the amount of oil that is recovered from the reservoir. This incremental oil will otherwise be left behind in the reservoir. Hence, in an oil reservoir where the natural aquifer is large and strong enough to maintain the reservoir pressure, water injection is unlikely to significantly increase the oil recovery from the reservoir.

water breakthrough is concerned with oil production wells. when a layer of water under the oil layer channeling into the oil accumulation, it called water breakthrough or water coning phenomena.

the function of gas-oil separator is to separate the production fluids into their constituents such as oil, gas and water

I think you are asking: What were the basic factors that affect oil production in the petroleum industry? Perhaps more simply put: What makes oil production in any one area go up or down?

It is a good question.

Oil production goes up when new fields are discovered. It takes a long time (as long as 10 years) between discovery and actual production from the field. There must be sufficient oil in the field, as confirmed by wells, to justifiy construction of facilities.

Oil production can increase when an oil company decides to improve production through stimulating wells (acidizing, hydraulic fracturing) or injection of water or gas to provide more energy and displace the hydrocarbons. Pumps can also increase production.

No matter how much efforts are put into improving production, there is only so much oil so eventually oil production goes down. There is frequently an increase in gas and/or water with time.

Now, the broader question- is the production in the US or the world going up, leveling off, or into a decline? I have included a link that pulls together many ideas on this subject. If new sources of oil, like tar sands, are now economical, perhaps we are in the leveling off phase. Others believe that because many of the largest fields are currently in decline, US oil production has peaked and we are in decline.

See related link.