Historically, before PCs took over the world different computer systems, and sometimes even the same computers running different software, had different partition table formats.
Afaict Linux never had it's own partition table format*. Traditionally you would use whatever the native partition table format was for the computer you were running it on. Particularly for boot disks it was/is necessary to use a partition table that was compatible with the computer's boot process.
Nowadays, unless you are dealing with obscure or retro systems, mbr and gpt are probably the only partition table types you are likely to encounter.
msdos (aka "mbr") was the traditional partition table format on IBM compatible PCs running DOS and windows. It's still widely used today, though sometimes regarded as legacy. The main practical problem with it is it uses 32-bit sector numbers, so it cannot fully support drives over 2 TiB.
gpt was introduced as part of the EFI standard, originally designed for booting Itanium systems. While Itanium was largely stillborn, EFI and GPT lived on. Apple adopted EFI for booting Intel MACs, and some time later EFI evolved into uEFI and gradually took over from the BIOS for booting PCs.
gpt is used in conjunction with a "protective MBR". This prevents pre-gpt tools seeing the disk as unpartitioned. In some cases the protective mbr may be replaced with a "hybrid mbr" allowing mbr only software to see some of the partitions on the disk, this is only needed in unusual cases (mostly involving multiboot systems on older Intel MACs).
On a PC with a traditional non-efi BIOS (or a uEFI one operating in "compatibility" mode), "msdos" is the best supported partition table. Grub can boot a non-efi PC from a gpt disk, but as far as I can tell windows is not supported on such a setup and such a setup is considered non-standard.
On a PC with uEFI operating natively, gpt is the supported partition table format. Some uEFI implementations can apparently perform uEFI boot with a MBR partition table but this is non-standard.
Arm macs also use GPT, but with some additional complications. The Asahi guys seem to be the experts on that.
* Linux does have lvm, but lvm is not treated as a partition table type.