1. mouse pointer capture, so you can point to things of interest in the video;
2. scroll-back actions and position of scroll bar are recorded; and other GUI elements and actions like switching between terminal tabs;
3. audio! so you can talk about what you are showing;
4. a standard video format viewable in many media players, easily shared or hosted as a simple file, or uploaded to video sites.
No character copy and paste, though; you have to supply people with supplementary files or documentation if that is important.
Window recording is easy. Typically, the recording program lets you pick a window and some options like whether to capture audio. You hit a start button and get a countdown 4, 3, 2, 1 ... which gives you a chance to switch to that window and get settled and ready. When done, you click on some gadget to stop.
Recording a TTY doesn't all have to be "live action". You can play some canned content in the session. For that, the good old "script" and "scriptreplay" utilities are useful.