take a look at code line 61 to 77 in your SDK file
To bring up a bit light in the darkness:
The
Agent?function=AgentSpeakInChat&Auth='+AuthKey+'&Text='+encodeURIComponent(Text) is not to chat with "Denise", it will only speak the sendet "Text" aloud and print it in the chatbox (described in the SDK). So we can say it is absolute similar to the "
AgentSpeak" function and the difference is only that the text is printed in the chatbox.
The
Chat?function=ChatInput&Auth='+AuthKey+'&Text='+Text is to Chat with "Denise" like as you type text in the chatbox and press return. So you are able with this chat function to let "Denise" things do like a search in the web. As example when you say: "tell me more about Phil Collins", Denise give you all the important information about Phil Collins back and speak it aloud. You can also say "play music" and Denise play all the music which she found in your music folder.
Tip: If you get back a long text from a websearch or Denise has read all the information which was interesting for you, so you can say "stop talking" to get "Denise" be quiet.
I've tested "stop talking" also to my wife, but it doesn't work
Ok, I hope this clarify the difference between this two functions.