Original zlib code: https://github.com/madler/zlib/blob/develop/contrib/puff/puf...

The code of the article: https://github.com/ieviev/mini-gzip/blob/main/src/main.rs

Top level declarations of the C code:

    #define MAXBITS 15   
    #define MAXLCODES 286
    #define MAXDCODES 30
    #define MAXCODES
    #define FIXLCODES 288

    struct state

    local int bits(struct state *s, int need)
    local int stored(struct state *s)

    struct huffman

    local int decode(...)
    local int construct(...)
    local int codes(...)

    local int fixed(...)
    local int dynamic(...)
    int puff(...)

Top level declarations of the Rust code:

    const MAXBITS: usize = 15;
    const MAXLCODES: usize = 286;
    const MAXDCODES: usize = 30;
    const FIXLCODES: usize = 288;
    const MAXDIST: usize = 32768;
    struct State<'a> 
    struct Huffman<'a>

    fn decode
    fn construct
    fn codes
    fn fixed
    fn dynamic
    fn stored
    pub fn inflate

..that doesn't proves anything.

it's just convenient configuration macros and generic procedures names being reused to implement the steps for the DEFLATE algorithm.

There are only finites ways for you to express a piece of code in a language.