Identifying stars found in the Milky Way as having formed in situ or accreted can be a complex and uncertain undertaking. We use Gaia kinematics and APOGEE elemental abundances to select stars belonging to the Gaia-Sausage-Enceladus (GSE) and Sequoia accretion events. These samples are used to characterize the GSE and Sequoia population metallicity distribution functions, elemental abundance patterns, age distributions, and progenitor masses. We find that the GSE population has a mean [Fe/H] ∼-1.15 and a mean age of 10-12 Gyr. GSE has a single sequence in [Mg/Fe] versus [Fe/H] consistent with the onset of SN Ia Fe contributions and uniformly low [Al/Fe] of ∼-0.25 dex. The derived properties of the Sequoia population are strongly dependent on the kinematic selection. We argue the selection with the least contamination is Jφ/Jtot < -0.6 and (Jz - JR)/Jtot < 0.1. This results in a mean [Fe/H] ∼-1.3 and a mean age of 12-14 Gyr. The Sequoia population has a complex elemental abundance distribution with mainly high-[Mg/Fe] stars. We use the GSE [Al/Fe] versus [Mg/H] abundance distribution to inform a chemically based selection of accreted stars, which is used to remove possible contaminant stars from the GSE and Sequoia samples.