Most of the following definitions are from Eschmeyer, 1998 and are used with the permission of Dr W.N. Eschmeyer.
Allotype
A term designating a specimen of opposite sex to the holotype.
Cotype
A term not now to be used that formerly was used for either a syntype or paratype.
Holotype
The single specimen on which the taxon was based or the single specimen designated as the name-bearing (or primary) specimen.
Lectotype
A syntype later designated as the one name-bearing type specimen.
Neotype
The specimen designated as the name-bearing type of a nominal species or subspecies for which no holotype, or lectotype, or syntype, or prior neotype is believed to exist.
Paralectotype
The type specimens remaining after a lectotype is designated.
Paratype
Specimens of the type series other than the holotype.
Primary types
Holotypes, Syntypes, Lectotypes and Neotypes.
Secondary types
Non-primary types such as paratypes and paralectotypes.
Syntype
Each specimen of a type series (of equal rank) when no holotype or lectotype has been named.
Type
A term used alone or as part of a compound term used for a kind of specimen or taxon.
Type series
The original name-bearing specimens used to define a species-group taxon.
Type species
The (nominal) species that is the name-bearing type of a genus or subgenus.
Chirotype
This term is sometimes used to refer to type specimens before the manuscript is published. When the paper describing the species is published, the specimens are no longer chirotypes but become true type specimens (see above).
Genotype
This term has been used incorrectly for the type species of a genus.
Plesiotype
This term has been used for a specimen illustrated in a publication. These are not type specimens. Plesiotype was sometimes used by G.P. Whitley, one of the most famous of Australian ichthyologists. Whitley worked in the Australian Museum Fish Section from 1922 till 1964.
Topotype
This term has been used for specimens collected from the type locality after the original description of the species.