Yes, the dash pads have a different shape. The 65' is pretty much a straight across dash. The 66' has a wrap around effect. It has extended ears that droop down lower around the dash bezel, the radio, and the glove box door.
A 66' dash pad can be installed in a 65', but would require that 4 new holes be drilled in the 65' metal dash frame. These holes are needed in order for you to attach the aforementioned ear sections tightly to the dash.
IIRC, the 66 does not use the little eyebrow chrome that is found above the gauge bezel and the glove box door. There is probably some attachment differences there too.