What is the difference, you may ask, or perhaps you replied that you do both? So what is the difference between the two? The purpose of a lesson is to provide direct instruction that improves the students ability in the skills being taught. The role of the teacher is to observe how well the students are performing the tasks presented, and to make suggestions for improvement. Group, as well as individual feedback is given, as a way of providing differentiated instruction. By the end of the "lesson", the students should be performing at a higher level than when they began. For example, the teacher might present a lesson on dribbling skills in soccer. The students would be taught how to use the different surfaces of their feet to dribble the ball, techniques for changing direction, how to use body fakes to get past an opponent, etc. This lesson would involve all students using their own ball and practicing individually. By the end of the "lesson", the student's skill level should show improvement.
An activity usually involves the student in some form of game play, in this instance, perhaps a game of 3 vs 3 "Keep Away", where the students have an opportunity to apply their skill. Or it might be playing short sided soccer games. The role of the teacher would be to organize fair teams, set rules, resolve disputes, and in some cases, actually referee the game.
The problem that I see as I visit schools, is that most PE teachers engage the students in a variety of activities but never actually teach a lesson. In the example above, the students would be organized into teams and play the game without the lesson part. We see this approach in the large variety of web sites that offer lessons plans for the various grade levels. They are all "activity" oriented and often are described as "activities" for your PE class. The students enjoy them as they are having fun, and perhaps improving their fitness levels through the activity, but they do little to improve individual skills as they do not provide for differentiated instruction. If the activity is game oriented, the higher skilled students dominate the game with the lower skilled students being less involved.
Question? Do you have a "catalog" PE curriculum centered around the latest piece of equipment being promoted in the PE catalogs, and consisting of a variety of "activities" you have gotten off of "lesson plan" websites, or do you have a sequential program of instruction tailored to meet the needs if your students leading to successful participation by all in a variety of age appropriate activities? Food for thought.