SRP tells us that you should only have a single responsibility in a module.
ISP tells us that you should not be forced to be confronted with more than you actually need. If you want to use a print() method from interface I, you shouldn’t have to instantiate a SwimmingPool or a DriveThru class for that.
More concretely, and going straight to the point, they are different views on the same idea — SRP is more focused on the designer-side point-of-view, while ISP is more focused on the client-side point-of-view. So you’re basically right.
It all came from
The ISP was first used and formulated by Robert C. Martin when doing
some consulting for Xerox. Xerox had created a new printer system that
could perform a variety of tasks like stapling a set of printed papers
and faxing. The software for this system was created from the ground
up and performed its tasks successfully. As the software grew, making
modification became more and more difficult so that even the smallest
change would take a redeployment cycle to an hour. This was making it
near impossible to continue development. The design problem was that
one main Job class was used by almost all of the tasks. Anytime a
print job or a stapling job had to be done, a call was made to some
method in the Job class. This resulted in a huge or ‘fat’ class with
multitudes of methods specific to a variety of different clients.
Because of this design, a staple job would know about all the methods
of the print job, even though there was no use for them.
so
The solution suggested by Martin is what is called the Interface
Segregation Principle today. Applied to the Xerox software, a layer of
interfaces between the Job class and all of its clients was added
using the Dependency Inversion Principle. Instead of having one large
Job class, a Staple Job interface or a Print Job interface was created
that would be used by the Staple or Print classes, respectively,
calling methods of the Job class. Therefore, one interface was created
for each job, which were all implemented by the Job class.
@ http://en.wikipedia.org/wiki/Interface_segregation_principle#Origin