I know they are called Intelligent Personal Assistants, but are they some sort of subset (or even superset) of carrots?
First I just want to say that autocorrect made me laugh. While the personal assistants you mentioned arenāt long and orange, I would consider them chatbots.
Hereās @mattās definition of a chatbot in his article:
A chatbot is a service, powered by rules and sometimes artificial intelligence, that you interact with via a chat interface.
(via https://chatbotsmagazine.com/the-complete-beginner-s-guide-to-chatbots-8280b7b906ca#.ffjnwxemj)
Iād say using voice to talk to Siri/Cortana etc. can be considered a chat interface.
Googleās definition is as follows:
a computer program designed to simulate conversation with human users, especially over the Internet.
And Wikipediaās:
Chatterbot, a chatter robot is a type of conversational agent, a computer program designed to simulate an intelligent conversation with one or more human users via auditory or textual methods.
Iād say they all simulate conversation, seeing as they answer stuff ranging from āwhat is the weatherā to ātell me a jokeā and āhow are youā. So imo they are a subset of chatbots 
. New phone, So I have to train auto-correct all over again. It changed āgit repoā to āgirl responseā on Twitter! Iād have thought these keyboards would store my personal dictionary in the cloud, allowing me to download it anytime I change my phone. That canāt be asking for to much, right?
So, it seems Iāve been thinking along the right path then. However, where do we draw the line? Do voice activated apps count? Even if they donāt talk back to me, I could argue they are the software equivalent of a mute butler, no?
The definition of a bot is
A device or piece of software that can execute commands, reply to messages, or perform routine tasks, as online searches, either automatically or with minimal human intervention (often used in combination).
Siri, Alexa, Cortana, etc fit perfectly into that definition. So yes, they are indeed a type of chatbot. The only difference is instead of text itās audio.
I think we have a winner. Carrots it is.
What about voice activated apps? Would they qualify as mute butler chatbots? Is it a chatbot if all the chatter comes from me?
A āchatbotā is just a conversation with a bot, that conversation could be voice or text, so yes.
Canāt wait to see what carrots the chatbot will be all about
I agree that they are chat bots. just because their activated by voice doesnāt make them any less so than their text initiated counterparts.