Its developmental in that it aims to follow the same steps as a typical child, whilst recognising that ASD kids will be behind on these milestones. So its looking at emotional / social milestones rather than academic ones or motor ones. So step 1 is an ability to regulate oneself and be calm and share attention with others. So most newborn babies will learn to do this within 3 months but ASD kids with sensory issues could take years. So Greenspan says until the child can regulate their senses they can't enjoy interactions properly. Stage 2 is engagement and relating ie an ability to form attachments to others. Stage 3 2 way communication (not necessarily with words) so initiating etc moving on to longer back and forth communications, then onto levels 4 -6: language, problem solving, imaginative play, more abstract ideas etc. Greenspan thinks without the ability to be social and enjoy being with others then there is always something missing - you can rote learn the skills but won't have the desire to be social and enjoy the world. Children can cross levels ie might ignore their parent most of the time (ie not conquered level 2) but be able to speak (level 4 skill). So you play at the level they have not mastered, so would work on just simple to and fro interactions.
The difference is ABA is adult led / directed; whilst Floortime tries to follow the child's lead. I think this is hard to do without training / coaching unless you have a child who is quite engaged to start with. But you would start by just playing alongside or by obstructing the child eg if they like opening and shutting doors you would get on the way of the door. Levels 1-3 focus on sensory motor play eg rough and tumble, swinging games etc to get the child to enjoy being with others and Greenspan thinks that when this social link is established that the brain then is able to move on to develop more complex skills.
With ABA you'd teach a sort of script for play eg we got DS to copy us moving a car back and forth. Then when he had mastered that we added a sound so he had to move the car and go brum brum. Now we play on the floor using these concepts. The idea is these skills will become ingrained and he'll use them spontaneously eg at nursery and eventually with other children. So its quite artificial. With Floortime we'd be concentrating on sensory play doing things he liked and we'd only play with cars if that was something he chose.
Until I started ABA I bought into the idea that ABA would give DS skills but the social bit would be missing and that we'd have to do a Floortime sort of approach ourselves to work on this as well, but this has not been our experience. In fact ABA has made DS much more social. So at nursery he used to sit by himself or tolerate brief adult interaction but now he follows the staff around and insists on their attention and that change was within a few weeks of starting ABA. Within ABA DS will also ask much more now for social rewards (a hug or tickle) rather than tangible ones (a toy) and if we get a nice interaction going with a fun tickle game or something then we just break off from ABA and go with it. ABA is much better at pushing the natural play situations and working on social skills earlier now than a few years back and every skill we are looking to take into everyday life asap. I think ABA gave us a structure of how to spend time with DS whereas previously it just seemed like hours and hours stretching out before us where I could engage DS for just small snippets. Now DS has an expectation he will have lots of intensive 1:1 time and although it is skills eg imitating, listening, he enjoys it and enjoys the attention and being with us and I think that has spilled over into making him easier to play with outside formal ABA time. So for us the ABA skills have opened a door which means that we now have better quality "Greenspan" type interactions outside ABA and DS is less aimless and better at playing with toys etc. If we had just done Floortime I'm not sure we'd have seen that kind of progress that quickly. But definitely we use Greenspan type play as well.
For academics, teaching living skills (dressing, toileting) and working on speech ABA seems the obvious choice for us. I think you'd need to add a formal teaching method of some kind to Floortime to teach these skills.
Pivotal Response Therapy (Koegal) is ABA based but child led and from what I have read seems like a mixture of the two and claim very good outcomes.