Delete/Remove--
MODO has two functions for discarding selected elements from a model or scene, 'Delete' and 'Remove'. Both essentially do the same thing, but depending on the selection type, how they go about it will produce different results.
'Delete' is found in the menu bar under the 'Edit' menu or can be accessed by pressing the 'Del' or 'Delete' key on the keyboard. 'Delete' will universally discard any selected item, be it in the Shader Tree, Item list, Graph Editor or any of the selected components in the 3D viewport. When 'Deleting' a selection, the command eliminates the entire selection, such as with a polygon, it also removes the associated edges and vertices (though doesn't affect the components of surrounding unselected geometry).
'Remove' is found in the 'Geometry' menu and it intended to discard component selections only. When applied, the 'Remove' options will act the same as 'Delete except in the case of 'Edge' type selections. 'Deleting' an edge will also remove the associated polygons that relied on the edge, where 'Remove' leaves the geometry intact, simply removing the edge itself (example below).
Edge Selection | Delete eliminates surrounding polygons | Remove keeps associated polygon |