Tangible objects are used in Virtual Reality to provide human users with distributed haptic sensations when grasping virtual objects. To achieve a compelling illusion, there should be a good correspondence between the haptic features of the tangible object and those of the corresponding virtual one, i.e., what users see in the virtual environment should match as much as possible what they touch in the real world. This paper aims at quantifying how similar tangible and virtual objects need to be, in terms of haptic perception, to still feel the same. As it is often not possible to create tangible replicas of all the virtual objects in the scene, it is important to understand how different tangible and virtual objects can be without the user noticing. This paper reports on the just-noticeable difference (JND) when grasping, with a thumb-index pinch, a tangible object which differ from a seen virtual one on three important haptic features: width, local orientation, and curvature. Results show JND values of 5.75%, 43.8%, and 66.66% of the reference shape for the width, local orientation, and local curvature features, respectively. These results will enable researchers in the field of Virtual Reality to use a reduced number of tangible objects to render multiple virtual ones.