Bruce Wedlock replies: The reason there are so many types of adhesives is there are specific advantages you might want for your application. Some characteristics that might apply to your project are open time, curing time, water resistance, hard glue line, different materials and reversibility.
Polyvinyl acetate (PVA) glues like Titebond and Gorilla Wood Glue come in several varieties depending on need for water resistance and a hard glue line. They are used for general woodworking assembly. Open times are around 30 minutes and curing times about 24 hours.
Polyurethane glues like Original Gorilla Glue and Titebond Polyurethane Liquid Glue are moisture activated and foam into uneven surfaces as they cure. They bond virtually anything. They are 100% waterproof, remain permanently flexible and require a damp surface to bond.
For the toughest glue applications, two-part epoxies work best. They glue most materials, have strong gap-filling properties and are waterproof. They are used for boat building and furniture repairs that have loose joints. The open time can be from a few minutes to an hour depending on the hardener mixed with the resin. Typical epoxies come with a 30 minute open-time hardener and cure in 24 hours. For quick work there are 5 minute varieties. Epoxy is expensive but System Three T-88 is available in economical half pints.
For veneering and gluing curved laminates, a hard glue line is required. Unibond One and Titebond Cold Press have hard glue lines and block bleeding through thin veneers. Urea formaldehyde (UF) glues such as Weldwood also have a hard glue line but require mixing before use. UFs are used to glue plywood, particle board and MDF for interior applications.
Hide glue has been the traditional woodworking glue for centuries. While hot hide glue is more difficult to prepare and kept hot at 140°F, it has a hard glue line and works well with veneers. Being reversible by heating the joint, it permits antique furniture to be disassembled for repairs. Hide glue tacks quickly and open time depends on keeping the joint warm. Hide glue will not cause problems with finishing. Liquid hide glues such as Old Brown Glue are more convenient if you need hide glue, but it does not tack as quickly as hot hide glue. Open time is about 30 minutes and it cures in 24 hours.
Cyanoacrylate glue (CA) is the industrial name for what is commonly known as Crazy Glue or Super Glue. CA can only bond with a surface when there is moisture present. This means if the cyanoacrylate glue is placed on a perfectly dry surface, it will not stick to the surface or form a bond. This can be avoided by first lightly wetting a surface such as metal or tile which may not be moist. CAs cure instantly and can easily grab your skin. Acetone will dissolve the bond as well as remove glue residue from a surface. Shelf life is only about a month after opening.