Answer by Sergiy Kolodyazhnyy for Bash: How to determine whether terminal is opened by third-party app

As far as Visual Studio Code goes, there apparently is a way to set additional environment variables for the integrated terminal. So, set up Visual Studio to use this config:

"terminal.integrated.env.linux": {
  "visual_studio": "true"
}

And within ~/.bashrc:

if [ -n "$visual_studio" ]; then
    # do something for Visual Studio
else
    # do something else for other types of terminal
fi

In general, you could rely on the environment given to the bash process. For instance, the $TERM variable, and run a similar if..then...else...fi branch for [ "$TERM" = "xterm" ] or something else. On case-to-case basis, you can investigate the differences in the environment via running env in each console, save that to file as in env > output_console1.txt, and diff output_console1.txt output_console2.txt as suggested by dessert in the comments.