Aside from sizes, which are discussed elsewhere, here's a quick, basic breakdown of matchcover types
(not subject matter) by trademarked names. Note: for most of the more popular types, many manufacturers had their
own versions, but not all had particluar trademarks for them, so the latter wouldn't be listed here.

Die-Cuts
[Covers with custom-cut sides]
Cut-Outs
[Portion of cover is cut out or additonal parts added on]
Debossed
[Portion of design is pressed down into cover]
Embossed
[Portion of design is pressed up into cover]
Action
Jewelite
Jurgen
Contour
Model
Pocket Wallet
Display
Eez-L
Safety Tab
Cameo
Signet
Debossed

Emboss-O-Match

Feature
[Art work on match sticks]
Color Photo
Foil Printing
Filigree
[Bubbled surface]
Feature
21 Feature
22 Feature
Giant Feature
Poster Feature
Lucky Sticks
True Color
Photocolor
Photo Color
Amerikolor
Camera Color
Matchorama
Atlas Four Color
Diamond Four Color
Foilite
Signet
Foil Fab
Taffeta Foil
Orleans
Filigree
Rhapsody
Stipple Finish

Satin
[Satin-type finish]
Midget
[Miniature-type cover]
Giant
Jewel
[longer 30-stick cover]
Silktone
Satinote
Midget
Junior
Giant
Giant Feature
Jewel
Jupiter
Classique

Glossy
Double Length
[cover folds out to twice the lenth]
Florentine
[fancy raised-ink/bubbled design]
Lenticular
[3-dimensional design]
[moving images]
Mirro-Gloss
Double Length
Florentine
Lenticular

Matchtone
[top flap is diff. color]
Rainbow
[abolone shell-color effect]
Metallic
[metallic finish]
Uniglo
[deep, oily finish]
Matchtone
Rainbow
Taffeta
Metallic
Serrated Gold
Uniglo
Uniglo II

Self-Extinguishing
Waterproof
Peel-Off Label
Stickyback
[cover has adhesive strip]
Stop-Lite
Drunkard's Match
Sta-Dri
Aqua-Pruf
Extend 'n Ad
Piggy Back
Doubl-Stik
Kleen-Stik

[Drawings courtesy of Long Beach Matchcover Club; Steve Bailey illustrator]

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