The answer is simple, almost evident in the question. Here's why:
The shell zsh is not bash, it is a different shell. zsh will not use the default files built for bash: .bashrc or .bash_profile. These two files are startup configuration files for bash. zsh has its own startup configuration files.
You can find out more about them here on the zsh intro page:
There are five startup files that zsh will read commands from:
$ZDOTDIR/.zshenv
$ZDOTDIR/.zprofile
$ZDOTDIR/.zshrc
$ZDOTDIR/.zlogin
$ZDOTDIR/.zlogout
You had mentioned your aliases don't work, to fix this, apply your aliases here like so:
~/.zshrc
alias sz='source ~/.zshrc' # Easily source your ~/.zshrc file.
alias ls='pwd; ls --color' # Alias 'ls' to: pwd + ls + color.