Should be pretty simple. In order for 'Group 1' users to be able to publish to 'project 2' only not 'project 1'. You need to make sure the following setups:
- 'Group 1' every user's site role has to be 'publisher'.
- 'Group 1' has 'interactor' permission at 'project 1' project level
- 'Group 1' has 'Publisher' permission at 'project 2' project level
So what is difference between site role 'publisher' vs project level permission 'publisher'? You can think of site role 'publisher' as someone's legal rights to work in US, while project level permission 'publisher' as a job offer from a company. Even I have legal rights to work in US, I must have a job offer from a company before I can work there. On the other side, even I got an offer from company based in US, I should not be allowed to work there unless I have legal rights to work in US.
Thank you so much Mark for the answer and most importantly the way you explained the concept .