I've edited 2 point layers with the Refactor Processing tool in QGIS 2.18.5 to re-order and edit the attribute fields so both layers will merge without creating additional fields in the merge. With both point layers saved with the same CRS, the merge tool gives me the error that 'All layers must have the same geometry type!'
I've also checked the field types match up (integer, string etc) which they do. I've tried with the raw data, before changing the order of fields in the attribute table but still no luck. I currently have no issue merging other shapefiles.
An additional observation: I've noticed when my data goes out of the field of view within the map canvas, the icon in the layers panel changes from a single dot to 3 smaller, unfilled dots (the same icon when categorising the styling of point data).