What makes the ArcGis online accurate when Arcmap is not?

[WilliamWarnick]

I have a geodatabase with feature classes projected with WKID:27561 NTF_Paris_Lambert_Nord_France. I wanted to 

use these features in Arcgis online. I transformed them to WGS84 using the Arctoolbox, zipped them into shapefiles and imported them into Arcgis online. They worked perfectly on the basemap and the distance between point features was correct. When I downloaded the same shapefiles and opened them in Arcmap the distances were off by 30%. 

I tried selecting a projection for the data layer but with no luck. What makes the ArcGis online accurate when Arcmap is not? Thanks in advance

[DanPatterson_Retired]

The ones you loaded in ArcMap should have been projected as well.  I suspect that when you loaded the file into arcmap, there was other data in the data frame.  Never assess the accuracy etc of any data that gets after other data has already been added to a data frame.  First file in sets the 'rules' by establishing the coordinate system etc. 

Always use the Project tool in ArcToolbox to convert from Geographic coordinates to planar coordinates (ie metres).  Define Projection should only be used when you get a warning that the coordinate system is unknown.  If you know what it is (not what you want it to be), then, and only then do you use it.