As you've noted, you get the same keycode. So the only way to distinguish them is to check the state of the Shift key in your event handling function. Of course, if you have more than 0.5 second delay between keypress and processing, you'll miss some hits.
Gvim doesn't do it because vim cannot do it (under normal circumstances). Sorry, but that's just how it is.
However...
Some terminals (e.g., xterm and iterm2) can be configured to send an arbitrary escape sequence for any combination of keys.
For example, add the following to .Xresources for xterm to send <Esc>[65;5u for CtrlShiftA. You can then map that in Vim to <C-S-a>. (65 is the decimal Unicode value for shift-a and 5 is the bit for the ctrl modifier. The u in this case stands for "unicode".)
As already pointed out, there are no ways to map <C-S-A> differently from <C-A>.
However, using tools like autokey (for linux & windows) or autohotkey (for windows), you can remap <C-S-A> to send a different key-stroke(s) for specific applications.
e.g. On my system, I have this setting in autokey:
$ cat ~/.config/autokey/data/gnome-terminal/ctrlshifta-gnome-terminal.py
#ctrl+shift+a sends '<S-F1>a'
keyboard.send_keys("<shift>+<f1>a") # Note that `f` in `f1` needs to be in lower case.
Then your ~/.vimrc can create mapping for <S-F1>a to do whatever you want.
Notes:
I have used <S-F1> as kind of leader key for detecting <C-S>. This was because my terminal did not accept <F13>-<F37> etc keys. If your application supports it, (gvim does I think) using those keys is recommended.
I mainly vim in gnome-terminal. So I used window class = gnome-terminal-server.Gnome-terminal as filter. Modify it to use gvim if you want. autokey supports a button for capturing any other window's properties like class/title.
Due to the way that the keyboard input is handled internally, this unfortunately isn't generally possible today, even in GVIM. Some key combinations, like Ctrl + non-alphabetic cannot be mapped, and Ctrl + letter vs. Ctrl + <C-I>1 + letter cannot be distinguished. (Unless your terminal sends a distinct <C-I>2 code for it, which most don't.) In insert or command-line mode, try typing the key combination. If nothing happens / is inserted, you cannot use that key combination. This also applies to <Tab> / <C-I>, <CR> / <C-M> / <Esc> / <C-[> etc. (Only exception is <BS> / <C-H>.) This is a known pain point, and the subject of various discussions on vim_dev and the #vim IRC channel.
Most terminal emulators treat control plus shift simply as control by default. Instead, you usually map those key combinations to an escape sequence and listen to that inside the terminal application.
Step 1: Configure your terminal emulator to bind Ctrl+Shift+A to the sequence Esc,A.
Your terminal emulator is the program that shows the actual window of the terminal. When accessing a server via SSH, the terminal emulator is a program on your local machine. Binding keys works differently in different terminal emulators. For example:
For urxvt, add URxvt.keysym.Control-Shift-A: \033A to the ~/.Xresources configuration file and reload it with xrdb ~/.Xresources.
For iTerm2, open Preferences -> Keys, add an entry, and bind Ctrl+Shift+A to the action "Send Escape Sequence" and type A into the field below.
Step 2: Bind Esc,A to a command in Vim.
Add the key mapping to your ~/.vimrc configuration and reload it with :source ~/.vimrc: