Difference between a rectifier diode and signal diode

Rectifier diodes can handle more forward current than signal diodes, and are more use in power supplies (like bridge rectifiers). Signal diodes are mostly used in lower voltage/lower current paths of the circuit. The 1N4148 is a typical signal diode and can only handle 200mA, while a rectifier diode like the 1N400x will work for 1A, the 1N540x even 3A.
Despite being designed for low signals the 1N4148 outperforms the 1N4001 for reverse voltage: 100V vs. 50V.

I guess by Lissajous pattern you mean \${I_F}/{V_F}\$ characteristics, showing the relationship between forward current and forward voltage. They always start at about 0.65V-0.7V, but for some diodes may be steeper than others. The 1N4148, for instance, will typically show a voltage drop of 1.2V at 400mA, whereas for the 1N400x this will be at 10A (pulsed). Rectifier diodes also tend to have higher reverse currents, typically \$\mu\$As versus nAs for the signal diode.

Both diodes work the same way by allowing current to flow in one direction. The differences have to do with power and frequency characteristics. They are made from a p-n junction and are two lead devices.

Small signal diodes have much lower power and current ratings, around 150mA, 500mW maximum compared to rectifier diodes, they can also function better in high frequency applications or in clipping and switching applications with short-duration pulse waveforms.

Rectifier diodes are designed to handle much higher voltage and current and are typically found in power supplies.

As far as the Lissajous patterns look like, they can be modeled in practically any simulation software. Check out LTSpice from Linear Technologies. http://www.linear.com/designtools/software/ . Plenty of tutorials and a large model library.