We derive ages, metallicities, and individual element abundances of early- and late-type galaxies (ETGs and LTGs) out to 1.5 Re. We study a large sample of 1900 galaxies spanning 8.6–11.3 log M/M⊙ in stellar mass, through key absorption features in stacked spectra from the SDSS-IV/MaNGA survey. We use mock galaxy spectra with extended star formation histories to validate our method for LTGs and use corrections to convert the derived ages into luminosity- and mass-weighted quantities. We find flat age and negative metallicity gradients for ETGs and negative age and negative metallicity gradients for LTGs. Age gradients in LTGs steepen with increasing galaxy mass, from −0.05 ± 0.11 log Gyr/Re for the lowest mass galaxies to −0.82 ± 0.08 log Gyr/Re for the highest mass ones. This strong gradient–mass relation has a slope of −0.70 ± 0.18. Comparing local age and metallicity gradients with the velocity dispersion σ within galaxies against the global relation with σ shows that internal processes regulate metallicity in ETGs but not age, and vice versa for LTGs. We further find that metallicity gradients with respect to local σ show a much stronger dependence on galaxy mass than radial metallicity gradients. Both galaxy types display flat [C/Fe] and [Mg/Fe], and negative [Na/Fe] gradients, whereas only LTGs display gradients in [Ca/Fe] and [Ti/Fe]. ETGs have increasingly steep [Na/Fe] gradients with local σ reaching 6.50 ± 0.78 dex/log km s−1 for the highest masses. [Na/Fe] ratios are correlated with metallicity for both galaxy types across the entire mass range in our sample, providing support for metallicity-dependent supernova yields.