What's the difference between the two? I mean as plants. They're translated into the same Polish word, but either has its own wikipedia article for example, so I'm a bit confused.
Technically, they might be the same thing.
In usage, a cane tends to be thicker and more rigid than a reed.
For me, the transition point would be somewhere around the consistency of a plastic drinking straw, give or take.
For musical instruments:
All bassoonists who have ever made reeds agree on a basic difference between “good” cane and “bad” cane. When two reeds are identical in design, manufacture and condition, the one that responds well is made of “good” cane, while the mediocre or worse reed is made of “bad” cane. Counting the Virtues of Bassoon Cane
If you do a Google search for: pith cane reed botanical, you'll probably find what you need.