Graphics and video
Scaling in relation to PC gaming loosely refers to how the game or video signal is affected by changes in the resolution or aspect ratio. The most common use case of the term is to attempt to describe how the field of view within a game is affected by changes in the aspect ratio, typically for the horizontal size of the resolution in relation to wider monitors (so 4:3 -> 16:9 -> 21:9). Another common use case of the term is to refer to how the graphics card or display handles a non-native video signal before displaying it.
A game designed for 16:9 will be letterboxed on a 4:3 or 16:10 monitor, while on a 21:9 monitor it will be pillarboxed.
A game designed for 16:9 will show more of the game world when played on a 21:9 (Hor+) and/or 16:10 (Vert+) monitor without losing any of the "reference" field of view it would have on a 16:9 monitor.
A game designed for 16:9 will show less of the top and bottom of the original intended field of view on a 21:9 monitor.
The game does not target any specific aspect ratio, instead it will show more additional information as necessary the higher the resolution is.
See Nonblurry (lossless, pixel-perfect) integer-ratio scaling for more information.
A game designed for 4:3 640x480 and displayed on a 16:9 1920x1080 monitor will be scaled by a factor of 2 up to 1280x960, followed by being pillarboxed and letterboxed as necessary to reach the 16:9 1920x1080 resolution.
Can be forced in games that support windowed mode using IntegerScaler (free) or Lossless Scaling (commercial).
A game designed for 16:9 will have vertically stretched objects (e.g. "thin" characters) on a 4:3 or 16:10 monitor, while on a 21:9 monitor those will instead be horizontally stretched (e.g. "fat" characters).
A game designed for 4:3 800x600 will be in effect be letterboxed and pillarboxed without any form of scaling on higher resolutions and other aspect ratios.
Maintain Aspect Ratio / Anamorphic
Expand Aspect Ratio (Hor+ in this case)
Crop Aspect Ratio (Vert- in this case)
Pixel-perfect scaling (integer-ratio scaling)
A scaling algorithm (sometimes referred to as a scaling filter or just filter) is a mathematical algorithm that is used when a resolution is stretched between the original resolution and the intended target resolution. As part of the scaling process, these algorithms might interpolate or resample pixels, affecting how the end results looks like. Technically any form of change in resolution can make use of an image scaling algorithm to influence how the end result looks like, but typically algorithms are only used when a pixel-perfect/integer-ratio scaling method is not available or used. Of the scaling behaviors described above, Anamorphic and Stretched in particular might often be combined with a scaling algorithm to "smooth" the end result.
In this mode the output stretches to fit the monitor, often with unwanted results (e.g. fat characters). Some non-widescreen games have a setting for use with this mode to make the stretched output have the correct widescreen aspect ratio; this is referred to as anamorphic widescreen.
In this mode the output expands to the biggest size while retaining its original aspect ratio. The unused space is left black.
In this mode the output displays at its original resolution. Graphics are sharp and have the correct aspect but the result may be very small depending on the resolution of the output and your monitor.