There are many types of spiders!
Spiders belong to an order of the class Arachnida. Other arachnids include: mites, ticks, scorpions, harvestmen, and others. The order Araneae (formal name for spiders) has over 45,000 named species. For a complete worldwide source for the classification of spiders, including all of the valid scientific names, consult the World Spider Catalog.
The order Araneae is subdivided into 114 families of spiders. In North America North of Mexico we have representatives of 68 these families. In Ohio we have a respectable 43 families and 645 species. For a quick overview of the 20 most common spider families in Ohio check this page.