We investigate one-halo galactic conformity (the tendency for satellite galaxies to mirror the properties of their central) in both star formation and morphology using a sample of 8230 galaxies in 1266 groups with photometry and spectroscopy from the Sloan Digital Sky Survey, morphologies from Galaxy Zoo and group memberships as determined by Yang et al. This is the first paper to investigate galactic conformity in both star formation and visual morphology properties separately. We find that the signal of galactic conformity is present at low significance in both star formation and visual morphological properties, however it is stronger in star formation properties. Over the entire halo mass range we find that groups with star-forming (spiral) centrals have, on average, a fraction 0.18 +/- 0.08 (0.08 +/- 0.06) more star-forming (spiral) satellites than groups with passive (early-type) centrals at a similar halo mass. We also consider conformity in groups with four types of central: passive early-types, star-forming spirals, passive spirals, and star-forming early-types (which are very rarely centrals), finding that the signal of morphological conformity is strongest around passive centrals regardless of morphology; although blue spiral centrals are also more likely than average to have blue spiral satellites. We interpret these observations of the relative size of the conformity signal as supporting a scenario where star formation properties are relatively easily changed, while morphology changes less often/more slowly for galaxies in the group environment.