The lights placed on the patio umbrella are simply of two types. The first one is called string lights and the second one is called lamp type.
These two are the only variation of patio umbrella lighting that are currently in the market. They are the only ones which will probably exist because the locations of these lights are either on the pole or on the ribs of the umbrella.
Rationally, these are the only parts of the umbrella that can possibly hold a considerable weight and in this regard, the lights. The possibility of installing lights on the canopy or the fabric of the umbrella has been studied but since the makeup of the canopy is not as sturdy as the pole or the ribs then they cannot be a reliable support to the lights that may be attached to them.
The reason why there has to be a sturdy support system for the lights is because they are designed to be attached to the umbrella permanently to eliminate the hassle of putting on and removing the lights whenever the umbrella is opened or kept away. On harsh weather conditions for example, the pole and the ribs of the umbrella can still hold on to the lights or the light bulbs while you are trying to put away or store the umbrella. The canopy may not be able to hold out for long and the weight of the lights plus the extreme weather may both damage the canopy and the lights.
To avoid that, string lights made of small light bulbs wrapped in a plastic insulation to prevent wetness and any short circuit of wires was developed. These are the lights placed on the ribs of the umbrella. Lamp types on the other hand are placed on the pole and are made of bigger sized light bulbs. Lights like these work on offset patio umbrella styles as well as standard models.