You can shoot standard foster type slugs out of any normal smoothbore shotgun....with some caveats. You usually don't want to shoot slugs with the screw-in full choke as a full choke is somewhat smaller than the diameter of the slug and the slug gets deformed passing through it. It can damage the choke or the barrel. An improved cylinder choke is ok because its not as much of a restriction.
Some shotguns, called "slug guns" have barrels made for slug shooting. they usually have rifle type sights and can be either smoothbore or have rifling in them. Sabot slugs are made to be used in barrels with rifling. Foster type slugs which are the traditional "deer slug" such as the Winchester super X are made to be used in smoothbores ,these slugs have grooves on the slug which are supposed to help stabilize the slug and make it easier to pass through the bore. I have heard two schools to thought on that: some people say that the grooves help the slug spin in flight, where some say it is only to reduce friction in the barrel. Sometimes these are called "Rifled Slugs". Brenneke Slugs are similar to Foster type slugs but have an integrated wad attached to the slug and more pronounced vanes(deeper grooves) on the sides of the slug. These are for smoothbores as well but are a little more sophisticated.