Xcode: Is there a difference between a framework and a pod in the project?

I'm just getting started with Xcode and iOS development. I am supposed to reproduce an iOS project on a tvOS. One of the frameworks is JSQCoreDataKit

In the original iOS project, this framework exists in two places:
PODS:.

FRAMEWORKS.

I installed the framework following the manual instructions in this link.
So in the new project, it is installed as a normal framework:
.

The problem I have faced is : Some of the code that works in the original project, relies on a code that is defined in the PODS folder:
EXAMPLE:

func saveChanges() {
    stack.mainContext.performAndWait {
        saveContext(self.stack.mainContext)
    }
}

saveContext function exists in:

And this is its definition(just in case):

public func saveContext(_ context: NSManagedObjectContext, wait: Bool = true, completion: ((SaveResult) -> Void)? = nil) {
    let block = {
        guard context.hasChanges else { return }
        do {
            try context.save()
            completion?(.success)
        }
        catch {
            completion?(.failure(error as NSError))
        }
    }
    wait ? context.performAndWait(block) : context.perform(block)
}

So while in the original project where Pods exists, this works fine.
In the new project, where it doesn't exist, and the framework is installed manually, I get this error:

Use of unresolved identifier 'saveContext'

But, the framework gets imported successfully with no errors :

import JSQCoreDataKit

One last thing, adding the framework with the manual method described in this link doesn't make it appear in here: