Eg. for segmentation, 0000:FFFF is equivalent to 0001:FFEF (Just a hypothetical case, don't know if we really use these in programming or if these are reserved spaces)
(I am new to assembly programming. Specifically x86.)
0000:FFFF is equivalent to 0001:FFEF only in real mode, VM86 mode, or SMM mode. In these modes, by definition, paging is not enabled. In protected mode1 without paging, they are necessarily translated to different physical addresses because the segment offsets are different (FFFF vs. FFEF) but the segment base address is the same2. With paging, when the segment offsets get added to the segment base address (which could be zero), they may either point to the same virtual page or different virtual pages, but either way, the the least 12 significant bits of the page offsets would be different (because the least 12 significant bits of the segment offsets are different) and so they cannot be equivalent irrespective of how the page tables are set up.
In general, different addresses may translate to the same physical address. When the page offsets are different but the least significant 12 bits are same nonetheless, it is possible for the logical addresses to get translated to the same physical addresses when they point to pages of different sizes. Otherwise, if at least one of the least significant 12 bits is different in the virtual addresses, they cannot be equal in the physical address space.
In protected mode, the segment selector 0000'0000'0000'00XXb is used as null segment selector and cannot be accessed. But Let's assume for the sake of argument that it is accessible (or consider 0000'0000'0000'0100b vs. 0000'0000'0000'0101b instead).
They refer to the same segment because the segment selector indices (the most significant 13 bits of each selector) and table indicators (the third least signficant bit) are equal