GAE will start up a machine occasionally to deal with increased demand and keep them on for 15 minutes at least. With something like Lambda (my old favourite was PiCloud) I can scale out to 50 processes for 10 seconds and only pay for 500 seconds of processing time.

For me, most of the benefit comes from data processing, where my usage is very bursty. The classic example used on most of the tutorials is image thumbnails/scaling/similar. All you want to say is "Do X to every file in this folder of 50k images" and let someone else handle starting and stopping as many machines as they can in order to get this done as quickly as possible.

No, heroku and to a lesser extant appengine are running at the whole application level. Lambda and google's, and azure's functions are literally individual functions that are deployed separately. They can be piped together to make a whole app but don't need to be.

One comparison I've heard is: can the platform spin up a new instance on demand in under 100ms? AWS Lambda can.

probably, but when I look at examples of companies using lambda, it seems rather generic.