What you should do now is define the districts data as Accra Ghana Grid using the layer's property page in ArcCatalog or the Define Projection tool.
Tom is correct that the spheroid-based GCS/datum of the first set of data could cause problems later.
If you continue to work at a relatively small scale, any offsets (correct or not) due to this incorrect definition won't be noticable.
My guess is that the first set of data came through ArcInfo workstation at some point as coverages or grids. ArcInfo Workstation uses a different 'projection engine'. If the datum isn't set, it defaults to Clarke 1866. When that definition is then converted to a shapefile or feature class, you get GCS_Clarke_1866. Because the rest of the definition doesn't match Ghana Grid, it's hard to say if the data is really based on Accra or Leigon or something else.
If you have some location where it's easy to overlay features to see if they line up, you might try modifying the coordinate system by changing Clarke 1866 to Accra (leave everything else the same) and see how they line up. If they're offset, try Leigon, set the data frame to WGS84, and set the geographic/datum transformations to convert from Accra and Leigon.
Melita