I understand how to use the "Clip" tool to an extent. Im just not sure how I would differentiate from the points inside and outside the polygon?
Would anyone be able to suggest or reference me to something that would help me understand?
simply do a select by location to get all the points within the buffer, then there is a switch selection option which will give you the points without...there are many other options...this is probably the quickest
I agree with Dan's solution. Also, if you want to create a new feature class for those outside you can either 'Create Layer from Selected Features' or 'Export Data' (ensure selected data is ticked). The first option will only create a cartographic layer of the selected, whilst the second option will create a whole separate feature class for the selected.
Another easy solution is a spatial join. Join the points to the polygon, polygon fields will be joined to the point table. Those points inside the polygon will take on the polygon attributes, and those outside will have null values in the polygon fields.
The Identity tool is the one you're looking for. There's a good article in the help that compares the different ArcGIS overlay tools.
An overview of the overlay toolset:
Haha! I love how the answers to this question perfectly illustrate the point that there are so many ways to get a task done in ArcGIS. We should see just how many we can come up with!