I just realized that you were probably mistaken in identifying the plugs I use. The second picture shows a mono audio phone plug while the other two are what Gerbing and I use.
Bingo- I did misidentify them (which is easy to do, since only the female was shown). You are using coaxial connections. Those will not suffer from shorting. Glad you are not trying to use a phone plug
The only problem with coaxial is that they typically don't have much "holding power" or "grip" and can very easily come unplugged.
Your first picture- I am not sure what those are called, but I have seen and used them before. I find them really frustrating because they grip SO well, they are often impossible to get them apart! And the connectors are often not serviceable, so they have to be completely replaced. They do have the advantage of being polarized, although that doesn't matter much with heated clothing.
I have a Widder vest also, and those connections are very solid. I am not sure what to call them, sortof a dual banana lead. The wires will come out of them eventually, or break. However, the nice thing is that they use screws to hold the wires in place; so they are extremely easy to repair and reuse. Attached is a picture of what Widder uses for those following along...