Most modules in Eve have several (up to tens) of variants (each a module in their own right), which fulfill the same basic function, but have different statistics. You can find all related modules through the in-game “Show Info” window, under the “related items” tab, where you can also compare the modules' statistics using the item comparison tool. Modules have an attribute (also visible in the “Show Info” window) called “Meta level”, which is roughly a measure of the module's quality - a module with a higher meta level will generally (but not always!) have better stats than the equivalent module with a lower meta level.
When shopping around for a module, it's recommended to use the item comparison tool to compare the module variants. While higher-meta modules tend to be better than lower-meta ones, there are plenty of exceptions, particularly for modules with many attributes (where modules will have different advantages and drawbacks compared to each other). Additionally, don't forget the cost - while officer and Deadspace modules will greatly outperform Tech 1 and Tech 2 modules, they often cost hundreds or thousands of times as much!
Module variants are grouped (as explained below) to make it easier to differentiate between them. You can tell which group a module belongs to by the little symbol in the upper-left corner of the module's image. Related modules all have the same base image, only differing in that symbol.
Civilian Modules are a special case and are only mentioned here for completeness. You should NEVER consider fitting a Civilian Module except in the Tutorial Missions and on your trusty Rookie Ship. These modules are useless except for educational purposes.
These are the basic modules that are manufactured by players from blueprints seeded on the market by NPCs. Meta 0 modules have no Meta level attribute visible in their attributes. They have generic names based on their type such as “1MN Afterburner I”.
If someone offers you a “meta 0” duel, they mean a duel in a Tech 1 ship with only this type of module installed.
These are dropped by NPC ships and are not manufactured by players. The higher the meta level the better quality the item. Higher meta level items are more effective and usually have lower fitting requirements as well, but this is not always the case. Meta level 1-4 items do not require more skills to use than meta 0. Because of their better performance higher meta level modules will have a higher price on the market.
These modules have more colorful names such as “10MN Monopropellant Enduring Afterburner” and “150mm Light Gallium Machine Gun”, and are therefore also called “named” modules.
After the module tiericide, named modules will have adjectives in their names which describe the main aspect in which they differ from their Meta 0 counterparts.
For example, the Large Shield Extender I (Meta 0) module has two “named” variants, the Large Azeotropic Restrained Shield Extender and the Large F-S9 Regolith Compact Shield Extender. When compared to the Meta 0 module, the former has a reduced signature radius increase, while the latter has reduced fitting requirements. Additionally, both modules have higher shield hitpoint bonuses (the module's primary attribute). Note that the additional adjectives in the module names (such as “Azeotropic”) are purely flavor text and have no specific meaning.
Often shortened to “T2”, these modules are manufactured by players through the Invention process. T2 modules are usually more effective than Tech 1 Meta 4 modules, but sometimes they are identical (and, in rare cases, slightly worse). Tech 2 modules usually require more skills to use than Tech 1 modules, and they usually take more CPU and/or Powergrid to fit. T2 modules have a meta level of 5. When deciding whether to use a Tech 2 module, make sure to compare it to a Tech 1 Meta 4 module before making the purchase. In some cases the meta 4 module has the same performance with lower fitting requirements.
Storyline modules are rewards from missions, specifically COSMOS missions and some Epic Arc missions. In COSMOS missions you don't get the item itself, but you receive 3-run Blueprint Copies (BPCs) that need some decent skills and sleeper technology to produce and most of them are quite expensive (in ISK and skills) to produce. Epic Arc rewards are given as items but their availability is limited to how often you can do the epic arc, and the time it takes to complete them. As such, both types of storyline items tend to be expensive despite being similar quality to Tech 2, and are not traded in great numbers.
Faction modules are equal or superior to Tech 2 modules and are purchased from Loyalty Point stores either as items or blueprint copies. These items will have a meta level of 6-12 (although most have a meta level of 6-9). They have names based on their faction such as “Caldari Navy Ballistic Control System”. They tend to require the same skills to use as Tech 1 items. You can identify a module's origin (i.e. which loyalty point store(s) you can buy it from) by its name:
Deadspace and Officer modules are dropped in Deadspace complexes and as loot drops from rare named enemies (which can be found, for instance, in asteroid belts or DED complexes in nullsec). These are the best modules and as such are very expensive. These items have a meta level of 7 or higher (although most have at least a meta level of 9). Deadspace modules have names based on their faction (using the same nomenclature as the NPC rats) and quality such as “Pith B-Type Large Shield Booster”. The progression from lower to higher quality is: “C-Type”, “B-Type”, “A-Type”, “X-Type” - so a “B-Type” module will usually be better (and more expensive) than a “C-Type” module, but you should always check the detailed stats. Officer modules are named after the NPC they drop from, such as “Estamel's Modified Multispectrum Shield Hardener”. While officer modules are usually better than Deadspace modules, this is not always the case; always check the attributes before you buy.