Unlike your usual methods of distinction like a dot or a slash in the center, or a narrower shape, this style uses horizontal stress. Good examples of it are the Academica, Turquoise fonts. I'm interested to know how it was originated, and its name, if it has one.
It's still a digit zero, it's just a different interpretation of one. Because it's a homoglyph care must be taken to represent it properly.
This "style" is becoming more common because of the disadvantages that a slashed zero has:
- The slashed zero causes problems in all languages because it can be mistaken for 8, especially when lighting is dim, imaging or eyes are out of focus, or printing is small compared to the dot size.
- It causes problems for some Scandinavian languages — Ø is used as a letter in the Danish, Faroese, and Norwegian alphabets, where it represents [ø] or [œ].
- It also resembles the Greek letters Theta and Phi in some fonts (although usually, the slash is horizontal or vertical, respectively).
- The symbols Ø and "∅" (U+2205) are used in mathematics to refer to the empty set.
- "⌀" (U+2300) is Unicode's codepoint for the diameter symbol. In German-speaking countries, Ø is also used as a symbol for average value: average in German is Durchschnitt, directly translated as cut-through.
Most current type designs carefully distinguish between these homoglyphs, usually by drawing the digit zero narrower and by drawing the digit one with prominent serifs. Early computer print-outs went even further and marked the zero with a slash or dot—leading to a new conflict involving the Scandinavian letter "Ø" and the Greek letter Φ (phi). The re-designing of character types to differentiate these homoglyphs, taken with the dwindling number of keyboard operators trained on mechanical typewriters, has seen a decline in these particular homoglyph errors. The degree in which two different characters appear the same to a given observer is called the "visual similarity".
Helfrich, James; Neff, Rick (2012). Dual canonicalization: An answer to the homograph attack. eCrime Researchers Summit (eCrime), 2012.
I think the other answer gave you the origins of the glyph style. Just to add to the information, that style of glyphs are called reversed contrast, reversed stress or sometimes French Clarendon.