You must know that:
Introns are non-coding regions of an RNA transcript, or the DNA encoding it, that are eliminated by splicing before translation.
An exon is any part of a gene that will encode a part of the final mature RNA produced by that gene after introns have been removed by RNA splicing.
Now, about the exceptions, alternative splicing: Here,
particular exons of a gene may be included within or excluded from
the final, processed messenger RNA (mRNA) produced from that gene. There are numerous modes of alternative splicing observed, of which the most common is exon skipping. In this mode, a particular exon may be included in mRNAs under some conditions or in particular tissues, and omitted from the mRNA in others.
Apparently, this greatly increases the biodiversity of proteins (since there are differences in their amino acid sequence and, often, in their biological functions) which might explain why it is so common.
So in this case, it becomes easier to understand if you use 'coding' and non-coding' as the difference instead of 'spliced' and 'not-spliced'.
EDIT- The coding region of a gene:
In DNA, the coding region is flanked by the promoter sequence on the 5' end of the template strand and the termination sequence on the 3' end. Although this term is also sometimes used interchangeably with exon, it is not the exact same thing: the exon is composed of the coding region as well as the 3' and 5' untranslated regions of the RNA, and so therefore, an exon would be partially made up of coding regions. The 3' and 5' untranslated regions of the RNA, which do not code for protein, are termed non-coding regions.
I had previously forgotten about the UTR's, so I have included that. Now, if there is a definite sequence where coding regions are found, it points out to the fact that coding regions must be intrinsic. Another point in favour:
The evidence suggests that there is a general interdependence between
base composition patterns and coding region availability.The coding
region is thought to contain a higher GC-content than non-coding
regions. There is further research that discovered that the longer the
coding strand, the higher the GC-content. Short coding strands are
comparatively still GC-poor, similar to the low GC-content of the base
composition translational stop codons like TAG, TAA, and TGA.