This solution is also based on a QGIS virtual layer and ideas from Finding nearest neighbors between two tables with point locations in SpatiaLite?
SELECT a.id, b.name, min(ST_Distance(a.geometry, b.geometry)) AS distance, a.geometry
FROM points_exact AS a, points_near AS b
GROUP BY a.id
ORDER BY a.id
From the SpatiaLite 4.2.0 SQL functions reference list:
ST_Expand - returns the rectangle bounding g as a Polygon. The
bounding rectangle is expanded in all directions by an amount
specified by the second argument.
There you can set your offset search value (0.7m).
The result is a temporary layer with the id from the layer
points_exact with the attribute
name of the
points_near layer and the distance. You can right click
Save As to a new vector layer (shapefile).
I really recommend not to use the
ST_Buffer function for larger data sets. In a test case I did a query on two point layers, each with a feature count of over 7000 points. Using
ST_Contains took about 3 minutes. With
ST_Buffer I killed the QGIS process after half an hour. I also recommend to disable rendering (bottom right of the QGIS Canvas) before running the query and adding the results to the project because it takes the same amount of time to render the features. Without rendering you can easily right click and
Save As immediately.