Both names sound similar, but their structural behavior is opposite. You can select them from the “Stiffness Type” list in the “Main” tab of the “Surface” dialog box.
Membrane: The surface has uniform stiffness in all directions, but only transfers membrane forces in tension (n_x, n_y) and membrane shear forces (n_xy). Under compressive and shear forces, as well as under moments, the affected surface elements are deactivated. A typical application is a foil or a tent roof that can only withstand tension.
Without Membrane Tension: Exactly the opposite. Only moments and membrane forces under compression are transferred. Once membrane forces cause tension, the affected surface elements are deactivated. A typical application is a hole bearing, that is, the modeling of shear-hole bearing connections where sheets and bolts come into contact only through compression.
Technical background on “Without Membrane Tension”: The plate stiffness, including the shear stiffness perpendicular to the surface plane, is linearly elastic; the plate stiffness in the surface plane is nonlinearly elastic according to the Drucker-Prager material model. The yield tensile stress f_y,t approaches zero when the hardening modulus E_p is small; the yield compressive stress f_y,c is set high so that compression is transferred in a practically unchanged, linearly elastic manner. Because this type modifies the degrees of freedom of the plate, it is only available for the 3D, 2D - XZ, and 2D - XY model types. The name has been changed once: in RFEM 5.06.1103 dated February 4, 2016, “Without Tension” was renamed to “Without Membrane Tension.”