Logical address space non-contiguous or Physical address space non-contiguous?

First of all, I'm a beginner in operating system.

What makes me really confused are the terms logical address space and physical address space.

In paging and segmentation, I thought logical address space of a process is something that is local so that it is contiguous while physical address space of a process may be non-contiguous. However, several lecture notes on the online seems to use such terms as if they are interchangeable. Are they really interchangeable terms or my understanding is correct?

Both slides are saying the same thing but in different ways. The slide on the left is saying that the logical address space can be non-contiguous with respect to the physical address space, which means that contiguous logical pages may or may not be mapped to contiguous physical pages. The slide on the right is saying tat the physical address space can be non-contiguous with respect to the logical address space, which means the same.

The logical address space of a process is flat; it ranges from zero to the maximum address. Similarly, the physical address space of the system is also flat. It is the mapping between them that can be non-contiguous.