Plantar simply refers to a location- the bottom of the foot. A wart is a benign growth caused by the Human Papilloma Virus. On the plantar surface they tend to be pushed inwards due to weight bearing and therefore are more painful than in non-weight bearing areas. Many times warts will appear to have small black spots in them which are thrombosed capillary ends. The skin lines are also gone in a wart. Plantar fasciitis is the inflammation of the tendon like band that supports the arch. It is unlikely that it would be a bump on the bottom of the foot.
There are many treatments for both these conditions. Surgery is not the only choice for either of them. As far as not having insurance, I can't really tell you you must see a podiatrist, but really, you should. Discuss your concerns and options and go from there.