Students' understanding of the orbital concept has been subject to considerable research and debate and often found at variance with a quantum mechanical ideal. Could it be the case that orbitals as actually used by practising chemists in teaching and research also differ from that ideal? Our experience shows that this might often be the case. Through a series of examples of pictorial representations of orbitals found in textbooks and other educational materials, as well as in research papers, we argue that this is a common situation, which deserves to be stated explicitly. We point out that, in particular, there is a way in which orbitals are frequently employed deeply rooted in chemical thinking and compatible with a classical (in the sense of pre-quantum) approach. Many chemists employ quantum-like terms, and rely on concepts that look quantum, such as "orbital", but they actually play on the well-known ground of the classical structural ideas that can be traced back to the work of pioneers like Cannizaro, Kekulé, or van't Hoff. We maintain that given the fundamental role of these semi-classical ideas in chemistry, it is nothing but natural to treat them in an equivalent fashion in chemical education.