I have had no luck snapping points from one layer to another line layer in both QGIS 2.18 and 3.6.3. The snapping plugin is enabled and editing is on for both layers but there are no 'Apply' or 'OK' buttons.
The snapping settings allow you to manually snap a vertex in one layer to the vertices and/or segments of another layer, while digitizing. This is good for snapping one vertex at a time.
But it sounds like you want to snap all the features in one layer to the features in the other layer. The snapping toolbar settings are not the right tool for that. Instead, use a Processing Tool, such as
Snap geometries to layer.
This algorithm snaps the geometries in a layer. Snapping can be done either to the geometries from another layer, or to geometries within the same layer. A tolerance is specified in layer units to control how close vertices need to be to the reference layer geometries before they are snapped. Snapping occurs to both nodes and edges. Depending on the snapping behavior, either nodes or edges will be preferred. Vertices will be inserted or removed as required to make the geometries match the reference geometries.
Like most processing tools,
Snap geometries to layer creates a new layer. By default the new layer will be a temporary layer, which will be deleted when you close the QGIS project. Be sure to save the temporary layer as a permanent layer before closing the project.