Is traveling from AMS or CDG airports to any Irish airport considered as a domestic flight or and international flight?
In other words, do I have to pass through the security check in the transit or I will only change terminals or gates?
Since AMS (Amsterdam Schiphol) is in the Netherlands and CDG (Paris Charles De Gaulle) is in France, both in the Schengen area, any flight to Ireland, which is not in the Schengen area, will definitely be considered as an international flight.
Domestic flights are usually defined as flights within the same country, but flights between two Schengen countries can be considered domestic as well. However, this is not the case for Ireland.
Regarding the security check, I believe it depends on the specific airport and from where you are connecting. At CDG I was once allowed to board a flight to the USA connecting from an international flight from Europe at a different terminal without passing through the security check again. At other airports, in a similar situation, I was required to go through security checks.
It would definitely be arriving into Ireland as an "international" arrival. Same as departing from Ireland to either to AMS or CDG. As such you would need a valid passport for this flight.
The only flights to and from Ireland that are classed as domestic are from within Ireland or the UK and you can travel on a EU issued driving licence or national identity card.