Push-To-Talk means that your microphone will only be activated when you hold down a key of your choice (which can be located in "Key Bindings"). This is often used when you only want one person to speak when playing particular games that requires a leader to call out actions so the team is more effective as an example.
Voice Activity Detection uses intelligent algorithms to determine that your input signal contains speech and allows you to speak whenever you like essentially. This is more suited to a casual community just wanting to have a chat while they're hanging out or playing games as an example.
Both of these settings can be found in the "Audio" section under settings.