Most "isometric" games are in fact "dimetric", i.e. follow a projection where 2 horizontal pixels match 1 vertical pixel when tracing straight horizontal or vertical lines.
The only difference is if you "stack" tiles vertically they slightly offset in 2d space from ones that are offset 1x+1y.
in an isometric projection all the edges of an axis-aligned cube are the same length. in the axonometric projection discussed here, which is dimetric rather than isometric, the vertical edges are of length 1 while the horizontal edges are of length √(1 + ½²) ≈ 1.118
is the fact that this projection is not isometric the reason zaxxon was called zaxxon and not zisom?
> The use of isometric graphics in video games began with Data East's DECO Cassette System arcade game Treasure Island,[6] released in Japan in September 1981,[7] but it was not released internationally until June 1982.[8] The first isometric game to be released internationally was Sega's Zaxxon, which was significantly more popular and influential;[9][10] it was released in Japan in December 1981[11] and internationally in April 1982.[8] Zaxxon is an isometric shooter where the player flies a space plane through scrolling levels. It is also one of the first video games to display shadows.[9]
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> In 1983, isometric games were no longer exclusive to the arcade market and also entered home computers, with the release of Blue Max for the Atari 8-bit computers and Ant Attack for the ZX Spectrum. In Ant Attack, the player can move forward in any direction of the scrolling game, offering complete free movement rather than fixed to one axis as with Zaxxon.