There is a special difference between 0.0.0 and 1.0.0. Let's dig into the Semantic Versioning standards. The following rules label these numbers as x.y.z:

**When x is 0** 

Chaos rules.

> 4. Major version zero (0.y.z) is for initial development. Anything MAY change at any time. The public API SHOULD NOT be considered stable.
>
>[Semantic Versioning 2.0.0](https://semver.org/)

**When x is greater than 0** 

Things start meaning things. 

>5. Version 1.0.0 defines the public API. The way in which the version number is incremented after this release is dependent on this public API and how it changes.
>
>6. Patch version Z (x.y.Z | x > 0) MUST be incremented if only backwards compatible bug fixes are introduced. A bug fix is defined as an internal change that fixes incorrect behavior.
>
>7. Minor version Y (x.Y.z | x > 0) MUST be incremented if new, backwards compatible functionality is introduced to the public API. It MUST be incremented if any public API functionality is marked as deprecated. It MAY be incremented if substantial new functionality or improvements are introduced within the private code. It MAY include patch level changes. Patch version MUST be reset to 0 when minor version is incremented.
>
>8. Major version X (X.y.z | X > 0) MUST be incremented if any backwards incompatible changes are introduced to the public API. It MAY also include minor and patch level changes. Patch and minor versions MUST be reset to 0 when major version is incremented.
>
>[Semantic Versioning 2.0.0](https://semver.org/)

So yes there is a magical difference between x going from 0 to 1 vs going from 1 to 2. People are funny about zero.

Of course many projects that still use 0 as their major are stable. The point is you weren't promised that stability by this version number. 

---

Not everything with a version number uses semantic versioning and may not follow these rules.  Read the documentation before making assumptions. 

Examples:  

Web 2.0, Super Bowl XXX, Star Wars Episode V. And just to round out this [“gigantic landscape”](https://softwareengineering.stackexchange.com/questions/440591/what-is-the-significance-of-reaching-major-version-1-0-0/440593#comment967488_440593) I give you: Mostly Harmless "The fifth book in the increasingly inaccurately named Hitchhikers Trilogy".

Sorry if I gave the impression that semantic versioning was universal.