(I have the same confusion. And I try to answer it based on my investigation/understanding.)

Possible Naming Schema

According to quote from ARM GNU Toolchain Downloads page, bare metal and Linux are two different targets. And to differentiate from the target architecture, I call it target environment. And my way to tell it is: if it has "linux" in the name, it targets Linux environment, otherwise bare metal.

Available for bare-metal and Linux targets

So I interpret the toolchain names with below schema:

...<host_arch>-<target_arch>-<vendor>-<target_env+abi>

1. Host OS: on what OS the toolchain itself runs. This is not part of the name but listed in the toolchain download page.

2. Host Arch: on what machine architecture the toolchain itself runs.

3. Target Arch: What machine architecture the toolchain's output targets.

4. Vendor: Who offers the toolchain.

5. Target Environment: can be bare metal or GNU/Linux.

6. ABI: things like call conventions for assembly functions. This is related to both architecture and OS (link). So far I have seen: eabi/elf/linux-gnu/linux-gnueabi

About the "target_env+abi" part

I think this is the most confusing part. ABI is related to machine architecture, OS and language (link). And I think below naming convention holds based on the both the Target Arch + Target Environment.

1. For AArch32 + bare metal, use "eabi".

2. For AArch64 + bare metal, use "elf". (similar to eabi)

3. For AArch32 + Linux/GNU, use "linux-gnueabi" (eabi generated by gcc)

4. For AArch64 + Linux/GNU, use "linux-gnu" (maybe similar to 3 just like 2 to 1)

So I think all 4 of them are about EABI. But may have some subtle differences.

Hope some guru can shed some light here.

Examples

Let's take some toolchain names from the ARM GNU Toolchain Downloads page as examples.

Example 1:
arm-gnu-toolchain-14.2.rel1-mingw-w64-i686-arm-none-eabi.zip

1. Host Arch = x86-64 because of the "mingw-w64-i686"

2. Host OS = Windows because listed so.

3. Target Arch = AArch32 because of the arm.

4. Target Environment = bare metal because no linux in the name.

5. Vendor: by open-source community, no specific vendor so it is none.

6. ABI = eabi

Example 2:
arm-gnu-toolchain-14.2.rel1-mingw-w64-i686-arm-none-linux-gnueabihf.zip

1. Host Arch = x86-64 because of the "mingw-w64-i686"

2. Host OS = Windows because listed so.

3. Target Arch = AArch32 because of the arm.

4. Target Environment = GNU Linux because of the "linux" in the name.

5. Vendor: by open-source community, no specific vendor so it is none.

6. ABI = linux-gnueabi

Example 3:
arm-gnu-toolchain-14.2.rel1-mingw-w64-i686-aarch64-none-elf.zip

1. Host Arch = x86-64 because of the "mingw-w64-i686"

2. Host OS = Windows because listed so.

3. Target Arch = AArch64 because of the "aarch64".

4. Target Environment = bare metal because no linux in the name.

5. Vendor: by open-source community, no specific vendor so it is none.

6. ABI = elf

Example 4:
arm-gnu-toolchain-14.2.rel1-x86_64-arm-none-eabi.tar.xz

1. Host Arch = x86-64 because of the "x86_64"

2. Host OS = Linux because listed so.

3. Target Arch = AArch32 because of the "arm".

4. Target Environment = bare metal because no linux in the name.

5. Vendor: by open-source community, no specific vendor so it is none.

6. ABI = eabi

Example 5:
arm-gnu-toolchain-14.2.rel1-aarch64-aarch64-none-linux-gnu.tar.xz

1. Host Arch = AArch64 because of the first "aarch64"

2. Host OS = Linux because listed in Linux-hosted section

3. Target Arch = AArch64 because of the second "aarch64".

4. Target Environment = GNU Linux because of the "linux" in the name.

5. Vendor: by open-source community, no specific vendor so it is none.

6. ABI = linux-gnu

To answer the original question

• aarch64-none-elf: is for AArch64 bare metal, vendor is none

• arm-none-eabi: is for AArch32 bare metal, vendor is none

Maybe aarch64-linux-gnu-gcc is not installed. Try

sudo apt-get install gcc-aarch64-linux-gnu

even I am also taking the same course, after trying for sometime, I am able to figure out how to install the cross-compiler, after referring to this link

https://gist.github.com/eltonvs/e7cd472dded89e7dcf4aea822e8121c1

in that page, they have given example with "gcc-linaro-arm-linux-gnueabihf-4.8-2014.03_linux.tar.xz"

in my case, I have downloaded "gcc-arm-10.2-2020.11-x86_64-aarch64-none-linux-gnu.tar.xz",

1. download gcc-arm-10.2-2020.11-x86_64-aarch64-none-linux-gnu.tar.xz, make sure that you download the correct file.

2. tar -zxf gcc-arm-10.2-2020.11-x86_64-aarch64-none-linux-gnu.tar.xz

3. then copy or move the folder which you get after untar to /opt/ directory

4. write a simple .c file and compile it using

   /opt/gcc-arm-10.2-2020.11-x86_64-aarch64-none-linux-gnu/bin/aarch64-none-linux-gnu-gcc a.c (give your sample .c file name here)

5. run below command to check if the binary is created for ARM or not.

   file a.out (give your binary name which got generated after compilation)