Confusion about the meaning of re and rπ
\$r_\pi\$ is an input resistance looking into the base with emitter terminal at AC ground. 



\$\Large r_\pi\ = \frac{d V_{BE}}{dI_B} = \frac{V_T}{I_B} = \frac{\beta}{g_m} = (\beta+1)r_e \$

On the other hand \$r_e\$ is an input resistance looking into the emitter terminal with the base terminal at AC ground. 



\$ \Large r_e = \frac{dV_{BE}}{dI_E} = \frac{V_T}{I_E} = \frac{r_\pi}{\beta +1} = \frac{\alpha}{g_m} = \frac{\beta}{g_m (\beta +1)}  \$

Sometimes because \$I_E \approx I_C\$ we can we can simplify our life and assumed that \$r_e \approx \frac{1}{g_m}\$   

http://www.ittc.ku.edu/~jstiles/412/handouts/5.6%20Small%20Signal%20Operation%20and%20Models/The%20Hybrid%20Pi%20and%20T%20Models%20lecture.pdf