The ***base game*** is usually the first complete released piece of content.  
It is also referred to at times as '**vanilla**', as in the unflavoured or basic flavoured version, but - as isanae rightly points out in the comments - this term is mostly used to set a game with or without any officially released content apart from a modded version.  
In some instances you can already get versions of a game which include additional and/or exclusive content (presented with cool names like Gold Edition, or Collector's Edition, the latter of which often features additional physical trinkets), or will include future content (which is often available separately as well). 

All DLC also often comes in the form of a so-called ***Season Pass***.

Newer releases can include more of the content that has been released in the mean time, like all DLC. For example, when a game has been selected as Game of the Year, it is usually rereleased in a Game of the Year or GOTY edition, and, as far as I know, always includes all DLC/the Season Pass.   
Sets including all available content from the get-go can be released as Ultimate Editions.  

A ***remaster*** or Remastered Edition is a game that has been updated in one way or another. This is often a graphical update, where models or textures are of a higher fidelity or resolution, new graphical effects like Depth of Field, Ambient Occlusion, DLSS, or Tay Tracing have been implemented, or a game simply supports higher resolutions. But a remaster can also contain new ir originally cut content, like how films have Director's Cuts.

Do note, however, that while they seem to adhere to a naming convention, editions with similar names do not always contain content you expect based on that convention.

***DLC*** is an abbreviation for **D**own**L**oadable **C**ontent.  
It is usually used for a sizeable chunk of new content for the base game, offering a large new questline, a new significant piece of game world, new gameplay possibilities, and so on.  

A game (or other piece of software) that was originally released on a specific platform (PC, PS, XBox, &c.) but later on (partially) rewritten and/or recoded for a different platform is called a ***port***.

A ***bundle*** is a relatively loose term: first and foremost I have to think about game bundles (e.g. the Humble Bundle) that offer a specific set or different tiers of games for certain price thresholds.  
But a bundle can also be a base game bundled with certain DLC or less significant content (centred around a distinguishing theme, for example), or a combination of games from a particular series or IP.