Spatial data sets store geometry. Spatial geometries are interval data - the origins for these data vary. Spatial data have X, Y, and (maybe) Z values stored within files associated with these data. There are other files, like projection files (PRJ) or world files (TFW) that help GIS sort out different coordinate reference systems (CRS) and allow the GIS to display spatial data in the same location regardless of CRS. The data geometries and the CRS files must match for a GIS to display data in the same location. If they do not you have a GIS problem.
GIS allow you to add data with different CRS but sometimes they need help figuring out what CRS these data are in. If you go assigning a CRS to a spatial data set without knowing what CRS the geometry is using you will not have data that align. This happens when data are shared without PRJ files or world files and you assign a CRS without knowing the correct CRS to assign. Check the metadata associate with your datasets (or contact the creators) to figure out what CRS these data reference before you choose one.
To understand whether your data are using the same CRS you should start a new QGIS project. Under project properties - CRS, uncheck enable on the fly CRS. Add your original data to this project. If they do not overlay, then these data do not share the same CRS.