We investigate the relationship between 5 GHz interstellar scintillation (ISS) and 15 GHz intrinsic variability of compact, radio-selected AGNs drawn from the Microarcsecond Scintillation-Induced Variability (MASIV) Survey and the Owens Valley Radio Observatory (OVRO) blazar monitoring program. We discover that the strongest scintillators at 5 GHz (modulation index, $m_5 \geq 0.02$) all exhibit strong 15 GHz intrinsic variability ($m_{15} \geq 0.1$). This relationship can be attributed mainly to the mutual dependence of intrinsic variability and ISS amplitudes on radio core compactness at $\sim 100\, \mu$as scales, and to a lesser extent, on their mutual dependences on source flux density, arcsec-scale core dominance and redshift. However, not all sources displaying strong intrinsic variations show high amplitude scintillation, since ISS is also strongly dependent on Galactic line-of-sight scattering properties. This observed relationship between intrinsic variability and ISS highlights the importance of optimizing the observing frequency, cadence, timespan and sky coverage of future radio variability surveys, such that these two effects can be better distinguished to study the underlying physics. For the full MASIV sample, we find that Fermi-detected gamma-ray loud sources exhibit significantly higher 5 GHz ISS amplitudes than gamma-ray quiet sources. This relationship is weaker than the known correlation between gamma-ray loudness and the 15 GHz variability amplitudes, most likely due to jet opacity effects.