In some cases, the classifier has become a lexical sign, such as in the case of "plane", in which classifier and sign coincide in handshape. However, one and another are distinguished by the context, the aspect, movement, etc.
"Planes are safer than cars."
"The hydroplane descended towards the lake, skimming the surface, and then rose again gaining height."
In the first example we see the lexical sign "plane", whereas in the second we see the classifier for "plane" within a construction expressing its flying movement regarding the surface of a lake.