Just my 2 cents, too.It is plain, meaning no contrast. Such as a "plain film of the abdomen", a film with no barium or gastrografin contrast.
One place where you might see "plane" is biplanar films, such as a biplanar angiogram. Images are made in two planes: From one side to the other (a lateral) and from front to back (AP), or back to front (PA), depending on what they want imaged. This gives a look at the structure from two perspectives. I believe a biplanar angiogram is imaged during one contrast injection (but I've been wrong before
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p.