Specialty lubes are still basically wet or dry lubes but are formulated for unusually extreme riding conditions or specific user preferences. The types of lubricants you may find in this category include wax, fluoropolymer, ceramic and biodegradable.
Lube Type: Wax
Wax lubes apply wet but then dry to create a protective coating around component parts. With each application the wax buildup increases, providing very good protection and lubrication. Wax lubes however are flaky, and require repeat applications to maintain effectiveness.
Lube Type: Fluoropolymer
Lubes that contain fluoropolymers(PTFE's) are typically dry lubes, however some wet lubes include PTFE's for added protection. Some lubes will include PTFE's as well as wax. PTFE's go on wet like a wax lube, but dry to form a thin film coating of protection. PTFE based dry lubes are also susceptible to washing off in wet conditions, but do not flake as easily as wax lubes. Most lubes with multiple additives will charge more for their products. Whether this added cost is worth it depends on how often and how far you ride, and how much time you want to dedicate to maintenance.
Lube Type: Ceramic
Ceramic lubes also come in wet and dry versions and vary in viscosity. Ceramic lubes include micro particles of Boron Nitride, a substance that lubricates in a way similar to graphite. This produces a thin protective layer that liquid or polymer based lubes cannot match. The carrier fluid will determine if the ceramic lube behaves like a dry or wet lube. Additional additives like fluoropolymers or wax can also determine the working properties of each type of ceramic lube. Viscosity may be a consideration mostly reserved for wet lubes. The idea being that a thicker, stickier lube will better adhere to surfaces during wet conditions, providing better protection.