What are the most usual Chinese terms for permanent markers vs. whiteboard markers Today in Chengdu I wanted to buy a replacement permanent marker pen for writing on cardboard.

I don't like nonpermanent markers because the ink can sometimes wipe off and stain your clothes. I find that in English the nonpermanent ones seem to be called whiteboard markers most often, and indeed that was written on most of the markers I could find in stores today.

But permanent markers were not easy to find and I found myself wanting to say something like "I want one of these but this is a whiteboard marker and I want a permanent marker".

These terms might not be considered basic enough vocabulary to be in most dictionaries. Google Translate translates them but I don't know if I can trust it.
As others have mentioned, when you are using borrowed words you can sometimes get stuck with misunderstandings especially if you go to a market or book store to buy this item rather than going to a stationary or art store.

My suggestion is to take a glossy piece of cardboard and then ask for a 马克笔 (mǎkè bǐ).

If you are provided with what appears to be a whiteboard marker I would politely test it on the cardboard and if it is a white board marker I would say 我要擦不掉的那种. I think this should get you what you are after.

我要擦不掉的那种 (wǒ yào cā bú diào de nà zhǒng) = "I want the kind that cannot be wiped off"

我要 = I want

擦不掉 = cannot be wiped off

的那种 = the kind

This might also help if they show you a thin marker pen:

我要粗一点的 (wǒ yào cū yīdiǎn de) = I want a thicker one