Everyone is checked when entering the Schengen area from outside the Schengen area, and when leaving the Schengen area to outside the Schengen area. That is true even if the other country involved is an EU country such as Ireland or Bulgaria.
EU citizens are subject to reduced checks, but they are nonetheless checked. Automated kiosks perform those checks in some places, but by no means in all.
Conversely, when traveling from one Schengen country to another, there are no systematic checks. There may be spot checks, but nobody gets an entry or exit stamp, and it's entirely normal to fly from one Schengen airport to another without seeing any government officers of any sort.
A system as you seem to imagine it could not exist, wherein some travelers must have their passports checked and others do not. In such a system, how would it be possible to prevent travelers who should be checked from going through with the travelers who aren't checked?
Schengen airports are typically set up so that part of the airport is designated for internal flights and part is designated for external flights. These parts of the airport are separated by immigration control points where passports are checked. The part of the airport for internal flights is separated from the outside by only a security checkpoint, while the part for external flights is separated from the outside by both security and immigration. (Some arriving passengers are also subjected to security screening, depending on the airport from which they are arriving.)
So, when a plane arrives in the Schengen area from Ireland or from Morocco, all passengers transferring to a Schengen flight or leaving the airport must go through passport control first. When a flight arrives from another Schengen airport, no passengers transferring to a Schengen flight or leaving the airport go through passport control.
At passport control, there are separate lanes for people holding EU, EEA, or Swiss passports. The kiosks will normally be there, if there are kiosks, in addition to some desks for people who cannot use the kiosks for some reason. The other lanes are marked "All passports"; anyone can use them.
You edited your question to ask
are there lanes of intra-EU travelers as well, no matter what passport is hold by them?
No: for intra-Schengen travelers, passport control is avoided by having those flights use the part of the airport that isn't isolated by passport control points. Since they're not passing through a control point, there's no need for a special lane. (For travel between the Schengen area and non-Schengen EU countries, everyone goes to normal passport control according to the passport they're using, because the travel is not within a unified immigration-control area.)