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It depends on how accurate you need the result to be, Diana.
MapInfo Pro allows you to create Drive Regions around a table of points. These regions can be based on time or distance. The Drive Regions are based on our GeoZone API. You would just know what drive region a point falls into and so not know the exact distance between the two points.
We also have a GeoRoute API that can give the drive time or distance between two points. Unfortunately, the GeoRoute API has not yet been built into MapInfo Pro.
Both these API require an account and some "credits" to work. As a MapInfo Pro user, you get 2000 credits each month that can be used.
Alternatively, there is the add-on MapInfo RouteFinder developed by Routeware. This tool allows you to do all sorts of analysis and calculations based on a routing network.