Oil lamp and butter lamp are not the same thing. Oil lamps generally use grease as fuel, and butter lamps use ghee as fuel. In some cases, oil lamps and butter lamps can be used as vessels to worship buddhas and bodhisattvas.
As for the lighting time, it can be decided according to personal circumstances and local customs. Generally speaking, lotus lanterns or oil lamps can be lit in the morning or evening to show respect and support for buddhas and bodhisattvas. In some special circumstances, such as prayers or ceremonies, lotus lanterns or oil lamps can also be lit at noon or other suitable time.