Electronic – Are \$h_{ie}\$ and \$r_{\pi}\$ the same thing

symbol [~]transistors

In my proving below, \$r_{\pi}=h_{ie}\$. Why two different symbols are created? It confuses beginner. Or, actually there are something different?

\begin{align*}
r_e &= \frac{26m}{I_E}\\\\
r_{\pi} &= \frac{26m}{I_E}(\beta+1)\\
&= \frac{26m}{I_E}\beta\\
&= \beta r_e\\
&= h_{ie}\\
\end{align*}

Two common equivalent circuits used for small-signal analysis of BJT are:

1. The hybrid-\$\mathbf{\pi}\$ model of BJT:
he hybrid-pi model is a linearized two-port network approximation to the BJT using the small-signal base-emitter voltage \$v_\mathrm{be}\$ and collector-emitter voltage \$v_\mathrm{ce}\$ as independent variables, and the small-signal base current \$i_\mathrm{b}\$ and collector current \$i_\mathrm{c}\$ as dependent variables.

Where \$r_{\pi}\$ is defined as,

$$r_{\pi} = \frac{v_{be}}{i_b}{\huge|}_{{v_{ce}=0}}\tag1$$

2. The h-parameter model of BJT:
Related to the hybrid-pi model, but using base current \$i_\mathrm{b}\$ and collector-emitter voltage \$v_\mathrm{ce}\$ as independent variables, rather than input and output voltages.

Where \$h_{ie}\$ is defined as,

$$h_{ie} = \frac{v_{be}}{i_b}{\huge|}_{{v_{ce}=0}}\tag2$$

From equations (1) and (2), it is clear that both \$r_{\pi}\ \&\ h_{ie}\$ represents the input impedance with output short circuited.

$$r_{\pi} = h_{ie}$$

But different symbols are used because they appear in different models.

Similarly,
In \$r_e\$- model of transistor input impedance is represented by \$\beta r_e\$.
In Y-parameter model input impedance is represented by \$(Y_{11})^{-1}\$.

The symbol used for parameters depends on the equivalent model used.