A BIM modeler knows how element with parameters are modeled and organized. For Revit this means understand the details levels when building and selecting RFA elements, by categories to best represent the design across many views.
A BIM coordinator utilizes collaboration platforms to check for clash and collision of elements. This may include BIM 360 Glue and BIM 360 enabled Navisworks to organize models by discipline or trade, in order to list clash and constructibility issues needing correct in the native files.
A BIM Engineer is a BIM coordinator that also oversees 3D model based shop drawings and fabrication either directly or by overviewing subcontractors .
A BIM Technician is a person who may be asked to do anything that is BIM or ITS related that is not understood by the company, but at some point an acronym was used to describe the problem.