Hi Katie, sorry for a long-waited response.
The boundaries service in Data & Maps for Puerto Rico are primarily based on one data source, while Street Map service is based on different data source. Boundaries data is more detailed than the Street Map data for Puerto Rico, which also is currently used in ArcGIS Online World Street Map service.
Our most recent update to the World Street Map includes more detailed data for Puerto Rico and aligns much better. We are planning to deploy this update to the World Street Map in early September, which hopefully should resolve the issue.
The only other difference is that the World Street Map is in Web Mercator �?? Auxiliary Sphere whereas the Data & Maps data is in GSC WGS84. ArcGIS is able to project the Data & Maps data to match the coordinate system of the World Street Map, just wanted to make sure that this is known.