Context. Evolved cool stars have three distinct evolutionary status: shell-hydrogen burning (RGB), core-helium and shell-hydrogen burning (RC), and double-shell burning (AGB). Asteroseismology can distinguish between the RC and the other status, but distinguishing RGB and AGB has been difficult seismically and spectroscopically. The precise boundaries of different status in the Hertzprung–Russel (HR) diagram have also been difficult to establish. Aims. In this article we present a comprehensive catalog of asteroseismic evolutionary status, RGB and RC, for evolved red giants in the Kepler field. To prepare this catalog we carefully examined boundary cases to define the lower edge of the RC phase in radius and surface gravity. We also tested different published asteroseisemic methods claiming to distinguish AGB and RGB stars against a sample where AGB candidates were selected using a spectrocopic identification method. Methods. We used six different seismic techniques to distinguish RC and RGB stars, and tested two proposed methods for distinguishing between AGB and RGB stars. These status were compared with those inferred from spectroscopy. Results. We present consensus evolutionary status for 18 784 stars out of the 30 337 red giants present in the Kepler data, including 11 516 stars with APOGEE spectra available. The agreement between seismic and spectroscopic classification is excellent for distinguishing RC stars, agreeing at the 94% level. Most disagreements can be traced to uncertainties in spectroscopic parameters, but some are caused by blends with background stars. We find a sharp lower boundary in surface gravity at log(g) = 2.99 ± 0.01 for the RC and discuss the implications. We demonstrate that asteroseismic tools for distinguishing between AGB and RGB stars are consistent with the spectroscopic evolutionary status at near the RC (with the asteroseismic large separation Δν ≤ 2 μHz), but that the agreement between the different methods decreases rapidly as the star evolves during the AGB phase. Conclusions. This work presents the most complete evolutionary status catalog for Kepler and APOGEE red giant stars. The data precisely defines the locus of RC stars in the HR diagram, an important constraint for stellar theory and stellar populations. We also demonstrate that asteroseismic tools can distinguish between AGB and RGB stars under some circumstances, which is important for the age estimation of field stars. However, we also put forward the importance of using several techniques to assess the evolutionary status determination for luminous red giants.