These are the URG and URG-N Training-Simulation grenades, intended for training soldiers in the methods of handling and throwing hand grenades.
The fuze is a modified UZRGM type with a simulation component in place of the detonator that produces a loud report and smoke.
The bodies are painted black with white markings. Fuzes are marked with purple paint.
The grenades are reusable.
The URG (Uchebnaya Ruchnaya Granata - "Training Hand Grenade") and URG-N (Nastupatelnaya - "Offensive") are specially made grenades to accurately reproduce the size and weight of their H.E. counterparts - the F-1 and RGD-5. In the case of the URG-N the body is made of cast iron rather that the sheet steel used for the service grenade.
Both have central body cavities which help amplify the report and provide an escape path for the smoke and gas.
The fuze has a longer firing pin to reach the special simulation component which is attached to an adapter bushing. This allows the fuze body to be re-used.
Paul has provided this photo of an East German training grenade with the original red paint. It has no threads in the top and a hole in the base. Made for throwing practice. Evidently made in large quantities, but they don't seem to show up here in the U.S. very often.
This one probably was sold in East Germany's sports shops with two grey rubber plugs in the open ends of the cast body.
(Thanks Erik & Alex for the details!)