How static modifier works in C?

I am trying to understand how the "static" modifier works in C, I went looking for its meaning and everything I found seemed a bit vague.

It is a modifier to allow the values of a variable to exist until the end of the program execution.

I understood what it means and its purpose, but beyond this definition I wanted to understand how it works underneath, so I generated the assembly of the C code

char    *thing(char *a){    char *b;    b = malloc(3);    b[0] = 'y';    b[1] = '\0';    return (b);}char    *some(int fd){    static char *a = "happened";    a = thing(a);    return (a);}

I create another code with non-static a variable and got this

/* With static variable */    .file   "static_test.c"    .text    .globl  thing    .type   thing, @functionthing:.LFB6:    .cfi_startproc    pushq   %rbp    .cfi_def_cfa_offset 16    .cfi_offset 6, -16    movq    %rsp, %rbp    .cfi_def_cfa_register 6    subq    $32, %rsp    movq    %rdi, -24(%rbp)    movl    $3, %edi    call    malloc@PLT    movq    %rax, -8(%rbp)    movq    -8(%rbp), %rax    movb    $121, (%rax)    movq    -8(%rbp), %rax    addq    $1, %rax    movb    $0, (%rax)    movq    -8(%rbp), %rax    leave    .cfi_def_cfa 7, 8    ret    .cfi_endproc.LFE6:    .size   thing, .-thing    .globl  some    .type   some, @functionsome:.LFB7:    .cfi_startproc    pushq   %rbp    .cfi_def_cfa_offset 16    .cfi_offset 6, -16    movq    %rsp, %rbp    .cfi_def_cfa_register 6    subq    $16, %rsp    movl    %edi, -4(%rbp)    movq    a.0(%rip), %rax    movq    %rax, %rdi    call    thing    movq    %rax, a.0(%rip)    movq    a.0(%rip), %rax    leave    .cfi_def_cfa 7, 8    ret    .cfi_endproc.LFE7:    .size   some, .-some    .section    .rodata.LC0:    .string "happened"    .section    .data.rel.local,"aw"    .align 8    .type   a.0, @object    .size   a.0, 8a.0:    .quad   .LC0    .ident  "GCC: (GNU) 12.1.0"    .section    .note.GNU-stack,"",@progbits

/* no static variable */    .file   "nostatic_test.c"    .text    .globl  thing    .type   thing, @functionthing:.LFB6:    .cfi_startproc    pushq   %rbp    .cfi_def_cfa_offset 16    .cfi_offset 6, -16    movq    %rsp, %rbp    .cfi_def_cfa_register 6    subq    $32, %rsp    movq    %rdi, -24(%rbp)    movl    $3, %edi    call    malloc@PLT    movq    %rax, -8(%rbp)    movq    -8(%rbp), %rax    movb    $121, (%rax)    movq    -8(%rbp), %rax    addq    $1, %rax    movb    $0, (%rax)    movq    -8(%rbp), %rax    leave    .cfi_def_cfa 7, 8    ret    .cfi_endproc.LFE6:    .size   thing, .-thing    .section    .rodata.LC0:    .string "happened"    .text    .globl  some    .type   some, @functionsome:.LFB7:    .cfi_startproc    pushq   %rbp    .cfi_def_cfa_offset 16    .cfi_offset 6, -16    movq    %rsp, %rbp    .cfi_def_cfa_register 6    subq    $32, %rsp    movl    %edi, -20(%rbp)    leaq    .LC0(%rip), %rax    movq    %rax, -8(%rbp)    movq    -8(%rbp), %rax    movq    %rax, %rdi    call    thing    movq    %rax, -8(%rbp)    movq    -8(%rbp), %rax    leave    .cfi_def_cfa 7, 8    ret    .cfi_endproc.LFE7:    .size   some, .-some    .ident  "GCC: (GNU) 12.1.0"    .section    .note.GNU-stack,"",@progbits

The question would be, what is happening and the difference between the two assembly codes and how does this behave at compile time and at program execution time.