I think we must view this from two angles. On the one hand, it could be the intentions of the teacher and this will equate to the aims of the lesson. On the other hand, it could be the goals of the learner, which might sometime converge with the planned outcomes. The ideal situation would be when the goals of learners converge with the planned outcomes of the lesson. That way, both learners and teachers would have the same goals and presumably, will be singing from the same hymn book.

At the moment I think we need to make a clear distinction between those two items.  I think they are related, but not the same.  The backdrop to this question is of course Assessment for Learning methodologies.  Certainly the literature and online resources use all sorts of terms and it is hard to reconcile them.

I want to think of Lesson Objectives as the thing that connects to the National Curriculum.  I dislike the way  that many of these statements are made.  "The children will learn how to add simple fractions."  Then somehow you are meant to measure whether they did or did not, usually by a2 test.  What we understand from the notions of Vygotsky and the ZPD is that concepts emerge gradually, not in a single lesson.  This is particularly the case when learning about fractions.  So I prefer lesson objectives like"Children will have the opportunity to develop their ability to add simple fractions."

The literature implies that learning intentions are what the pupils think they are learning.  Phrases like it should be in child friendly language is used.  It seems to me that this is becoming a mechanical process of teachers writing stuff on the board and kids writing it in their books, without the students knowing anything about what they are learning.  "We are learning how to feed a twiga."  Unless you speak English and Swahilli you would have no idea what that sentence meant  I am starting to think that establishing learning intentions starts with getting children engaged in the learning first and then getting them to pause for a moment and express what they think they are learning.

As a primary classroom teacher, I think it is simply adult pen pushers with clipboards playing with semantics. From discussions with children, all they want is to know is what they are supposed to be learning, and how to know if they have been successful. Whichever terminology is used doesn't bother them.

Actually it is researchers asking questions and trying to improve things and find smarter ways of teaching.  If you look at the BBC videos listed below you will see teachers who were willing to embrace AfL methods claiming that they got through the curriculum in half the normal time.  If you then watch the Ted Wragg video you will hear about the research which reveals that despite the evidence teachers continue in the same old fashion and make no improvement.  Everyone can improve what they are doing - if they think about it. 

Nobody is suggesting that the terminology concerns the children.  But it is important that we understand the concepts behind terminology and not just make it up.  I added a link to a blog which discusses the issue of writing objectives on the board - one of the practices done (not mandatory) with AfL.  There are 58 respondents to the blog.  It is an absolute muddle of teachers using the same words, but with radically different meanings.  Some of the teachers just see writing the objectives down as something they have to do because the administrators want to see it!  Worse still is we now make children write the objectives in their books.  Establishing learning intentions is about engaging children in their learning. 

https://www.youtube.com/watch?v=J25d9aC1GZA

https://www.youtube.com/watch?v=1iD6Zadhg4M

http://www.teachers-media.com/videos/hot-research-assessment-for-learning#video_title_bar

http://www.joebower.org/2011/10/stop-writing-objectives-on-board.html

I agree with you Dave on the broad principles you have raised. As a practitioner, what I find helps my children is when they have a clear understanding of what they are learning and why. What creates the problem is when teachers get into trouble with the 'clipboards' for not having a visible learning intention/objective (ie written  on the board or in books); and teachers who refuse to embrace change that enhances the learning of their class.

Strange but true: I have been marked down by a lesson observer in a PE lesson (outdoors) for not having the learning objective written on a board even though I had shared it with the children. This happened about six years ago but it did happen.

It is a problem.  I am not in the direct line of fire.  I design products, e.g. Roamer.  But I face similar pressures - to create things cheap and nasty but make a profit.  I refuse to do it, unless it makes educational sense.  Hence I insist of forming partnerships with excellent teachers and making sure what I do is supported by research.  I really believe that the Black and Wiliam stuff on AfL is effectively a summary of good practice and should be used to underpin the design of products and activities.  The trouble I have had with reading a lot of materials relating to Learning Intentions and Success Criteria is that it is becoming mechanised.  I am part of a group working on MESHGuides that summarise the evidence in a way that will allow you to present it to the person who marked you down.  The video below is an excellent rebuttal to the insistence that learning intentions should always be written.