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Caulking materials are sold in large (28 ounce) and small (10 ounce) tubes that are lined with foil or plastic on the inside surface, to allow the liquid to flow out easily. The caulking material will remain flexible after it cures / dries.
A caulking material may also be called a SEALANT. It is used primarily to close gaps that could allow air or water to penetrate into an assembly. For example, the gap that happens around the perimeter of a window where the trim meets the drywall may be SEALED with a caulking material like acrylic latex caulking.
An ADHESIVE material is used to glue things together permanently, so they can't be separated. One example might be when construction adhesive in a tube and caulking gun is applied to plywood subfloor when a house is being framed. These types of adhesives might be made of polyurethane monomers, acrylic resin or other glues.