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First of all, the distinction you make between "packers" and archiver programs (ZIP, etc) or compression programs doesn't appear to have any basis.

A "packed" executable cannot be executed directly. It must be unpacked first. This is exactly the same as (say) a ZIP file containing malware, or a malware file that has been compressed with a standard compression program.

What about a "packed" executable that has been created by a program that does the "packing" in a secret way ... to evade detection? Well that won't work. The malware still has to be unpacked before it can be executed. So that means that the bad gut now has a second problem: getting the unpacker onto the victims machine. And once someone (an anti-hacker) gets hold of the super-secret unpacker, it is no longer secret. It can be reverse engineered ... or simply used as-is by an AV product on suspicious binary files.

The only practical use of "packing" that I can think of is to add self-unpacking functionality to the malware. The malware (as distributed) would consist of an executable with a small amount of code that implemented the unpacker. The rest of the executable would be packed code that implements the nasty stuff. When the user runs the malware, it would unpack the packed code, load it into memory and start executing.

However, there are potential ways to detect or prevent this kind of thing.

• If the unpacker writes the executable code into a file prior to loading it, an AV product could detect that.
• If the packer attempts to load code into itself, there are ways that could be blocked; e.g. using memory protection hardware + the OS, etc to stop the unpacker from creating memory segments containing executable code; see https://en.wikipedia.org/wiki/Executable_space_protection.
• An AV could look for the signature in the packed code, or it cold look for a signature in the unpacker code.

In short, malware could use some kind of "packing" to hide itself, but there must be an executable component somewhere to unpack it.

If so, how can we say that these binaries are packed or not?

• If the malware is distributed as a non-executable you figure out what is going to unpack it, and then see if that process is going to give you an executable.

• If the malware is a self-unpacking executable, you reverse engineer the unpacking component to figure out how it works.