"Isit true that getting a smaller frame as compared to a larger frame will provide sharper and crisps vision?"
Nope, size doesn't matter. Assuming that the refraction is done properly, alot of times sharper and crisp vision is dependent on the type of frame (Plastic, Metal, with or w/o nose pads) chosen, Lens material used, light transmissibility of lens & vertex distance.
Also noticed that whenever I get tested, the vision on the test specs looks much sharper than after the spectacle is made. Any idea why this is so
Unless you have super high degree, usually what you see while using the trial frame should be the same as what you see with your specs.
For higher degree, opticians/optometrist would usually take more precaution as to what frame to recommend and would adjust the degree accordingly if the frame is too far/near the face. Trying choosing lenses which provide better light transmissibility.