Visibility of a family determines in which view the family displays and what it looks like in that view.
Typically, when an element is created by a family, the geometry of the element will change, depending on the current view. In a plan view, you may want to see a 2D representation of the element. In a 3D or elevation view, you may want a fully detailed 3D representation of the element. You have the flexibility to display different levels of geometry.
For example, you could create a door frame and use lines to represent it. Or you could extrude the door frame, so it has a 3D representation.
Detail Level determines the visibility of elements at different levels of detail.
For example, you might create a door with certain embellishments. You then may decide that the embellishments should only appear at a certain detail level.
You control the detail level in a project view with the Detail Level option on the view control bar. You can set the visibility and detail level of any 2D and 3D geometry in the family after you create it.
Families are either cuttable or non-cuttable. If a family is cuttable, the family displays as cut when the cut plane of a plan view intersects that family in all types of views. If the family is non-cuttable, it displays in projection, regardless of whether it is intersected by the cut plane.
You can determine if a family category is cuttable in the Object Styles dialog (click Manage tab
Settings panel
Object Styles). If the Line Weight Cut column is disabled, the category is non-cuttable.