Nope! It's common to confuse the two, but bamboo and wicker are not the same. Easy mistake to make, since both are used in furniture and home decoration goodies, but in technical terms, they're actually quite different. Bonus points to you if you already knew!
Wicker: Wicker is actually more of a weaving technique (and/or a catch-all term for a bunch of materials), rather than a name for any material in particular. When materials like rattan, water hyacinth, or bamboo get all twisted and shaped into patterns, that's 'wicker'. It's the technique, basically, not the material.
Bamboo: Bamboo is not a technique, of course, but a material (and popular panda bear cuisine). It is often used in wicker furniture, as flooring, and even comes in handy during construction; it's not uncommon to see scaffolding made from bamboo in some Asian countries. Pretty wild stuff (excuse the pun!). So, while used in wicker products, bamboo is distinct from the broader category of wicker.