IM is sometimes called chat, just like a phone call or even a web conference can be called chat.
But chat to me means a standing group chat that you might enter and leave and come back to. It's usually informal and often, but not always, unrecorded, so it's not good for assigning tasks and following up. It is good for one to many conversations, like if i need help with something and don't know who is available or who would know the answer, i can post a message in chat and wait for one of the people monitoring the chat to respond. Similar to an email alias but without spamming people's inboxes unnecessarily.
A war room chat is used for a specific problem solving or high risk event like if we are rolling out a new product or upgrading our software this weekend. People with problems pop in and people with answers are staffed to monitor the chat. War room chats can be accompanied by a war room web conference or you might choose one or the other.
Web conferences are when people share audio and video, and sometimes screen sharing. Usually people connect over the web but sometimes on the phone. Web conferences are great especially for people who like meetings and hate typing but I strongly prefer chat when everyone isn't going to be online at the same time. If you have a web conference and explain everything and have a big discussion about it then everyone there hears it... but anyone who's offline at the time is going to need to be updated later. If you do this stuff over chat, it's a hassle to do all that typing but anyone who checks in later can catch up on the discussion quickly and join in.
The web conference is much better for things that need immediate attention and either don't need to be recorded or can be listened to later. Usually someone gets stuck scribing the web conference or giving a detailed status later for people who didn't attend.
If you say shoot me a text or ping me later I hate you. I hate myself sometimes because I've heard them so much it just slips out.