Target - aim - goal. Same thing.
Yes, I believe it's very important to have targets. Without them, there is no direction and sometimes decreased motivation.
I do not talk openly with my students about what my specific aims are. I know what I'm looking for, and make corrections in their playing. I give them music to sight read that is at an appropriate level for them. In my view, the aims are for me - to keep things moving along and to make sure I'm teaching them the way I should.
As far as the order goes, I think it's important to be flexible, because each student is going to grasp concepts in a different order and at different rates. A teacher should have a mental checklist of what the student should be able to do and always be looking for those things and, if need be, finding ways to fill in the holes.
That being said, it's good to have a general order that most kids will follow. The order for reading music (that I use) is: grand staff and how each white key has its own line or space, middle C, measures, time signatures, note values, and then note names. They have to be able to say the letter, write it, and play it on the piano (with the correct rhythm). Steps, skips, and other intervals; reference notes, recognizing common chord patterns and scales, recognizing common rhythms; understanding how to analyze a piece before playing it, finding repeats, modulations, etc.
The order for playing is: clear and controlled movements in hands separate. Then, as soon as possible, have them start playing pieces with both hands at the same time. Coordination is a big hurdle in piano playing, and I like to get past that one right away. Start in five-finger C position, then branch out, making sure they understand how to use the right fingers for most efficient playing. Scales, chords, arppegios - how to position the hand and wrist and use them when playing black keys. Understanding how to approach the learning of a new piece.
I'm sure there's more. That's a start . . . concepts that I "aim" to have my students understand.