A Construction is any sculpture where a variety of materials are joined together to make a 3D artwork. An example would be below ("Soft Toilet", Claes Oldenburg, American, 1960's), where vinyl, wood and other materials have been used to build the artwork.
An assemblage is a particular class of construction. As in a construction, the artist is joining together a variety of materials. However, the materials in an assemblage are, more specifically, FOUND OBJECTS. That is, objects that were made by someone other than the artist, usually for a non-art-related purpose. The artist finds ways to combine these found items, often emphasizing the way they do not seem to belong together, and were never meant to be used in the manner the artist has chosen. Below is a good example of an assemblage: "Monogram", by Robert Rauschenberg, American, 1960's.