From below-Kylie
Taken straight from the help:
"Collector for ArcGIS focuses on data collection and provides a streamlined experience for working in the field, while the ArcGIS app focuses on general map use, query, and feature editing."
For a bit more info, you can also look at the differences with the ArcGIS app and Explorer, and many of the same differences apply with the ArcGIS app and Collector:
"ArcGIS for iOS and Android were the first native viewers of maps hosted in ArcGIS Online or Portal for ArcGIS. Explorer for ArcGIS is the modern, native experience for working with your organization's maps. As the ArcGIS system evolves, additional functionality will be brought into Explorer, while the ArcGIS for iOS and Android apps won't be updated with new features and functionality."