Please read also the important update from November 13!
AGP 4x / 2x and Operational Voltages
I. Obvious Characteristics
At the moment we find virtually nothing but AGP 2x und 4x graphic boards on the market. AGP (Accelerated Graphics Port) was a new bus-system for graphic boards, developed by Intel and relieving the PCI boards. Accordingly, Intel provides the specifications for AGP Specifications 2.0 (PDF) answering complexly almost any question (the stress is on 'almost'!) to be settled here.
We start with the optical comparison of AGP 2x and AGP 4x, strictly speaking the plugs of the graphic boards:

AGP 2x Graphics Board

AGP 4x Graphics Board
The two photographs clearly show the different notches within the golden pin strips. The AGP 2x board has only two, as demonstrated with a Voodoo5 5500, whereas the AGP 4x board has three of these notches according to Intel's specifications.
This should be a marked characteristic, but we'll see that it is merely a clue, not a certain determination. But it can be kept in mind that a graphic board with only two of the above depicted notches is definitely an AGP 2x board.
We continue with the different available AGP-sockets, which are of course based on the Intel specifications as well:

AGP 2x

AGP 4x

AGP Pro 4x

AGP Universal (1x / 2x / 4x)
The photographs demonstrate us the existing variations of AGP-sockets, but meanwhile the AGP 2x form is no longer found on actual motherboards. When looking at the pictures with AGP 2x and AGP 4x slot, we clearly see the shifting of the slot's bridge. The AGP Pro socket, which is a bit longer than a conventional AGP 4x slot due to an additional notch (which is usually protected by a small sticker to avoid the wrong installation of regular (i.e. non-AGP Pro) AGP 4x boards) was only included for completion, but is irrelevant for our article.
A comfortable but dangerous solution is the AGP universal slot. Motherboards using this slot and a chipset able to handle AGP 2x and 4x graphic boards accommodate users who are still owning an old AGP 2x board but like to upgrade in the future. Coming back to the cited press release regarding damages of mother- and graphic boards, this AGP universal slot becomes dangerous when the used chipset is not able to handle AGP 2x boards. To avoid misunderstandings: The possible damage is not caused by faulty installation but by unsuitable, too high voltage.
Please read also the important update from November 13!