What are an internal and external exons?
Yes, the internal exons are those that aren't at the ends, which are often referred to as terminal exons1. 

However, exons are sequences of nucleotides that are incorporated into the mature mRNA — i.e. they don't have to be (entirely) protein coding. 

It is probably simplest to think of exons as being the transcribed regions that are not introns — i.e. they are the sequences that don't get spliced out during transcript maturation.

In other words, the 5'UTR is typically§ part of the first exon and the 3' UTR is typically§ part of the last exon.

§Note: I say typically, because sometimes introns are found within the UTRs2,3.

Reference:

1: Bolisetty, M. T., &amp; Beemon, K. L. (2012). Splicing of internal large exons is defined by novel cis-acting sequence elements. Nucleic acids research, 40(18), 9244-9254.

2: Eden, E., &amp; Brunak, S. (2004). Analysis and recognition of 5′ UTR intron splice sites in human pre‐mRNA. Nucleic acids research, 32(3), 1131-1142.

3: Paolantoni, C., Ricciardi, S., De Paolis, V., Okenwa, C., Catalanotto, C., Ciotti, M. T., ... &amp; Giorgi, C. (2018). Arc 3′ UTR splicing leads to dual and antagonistic effects in fine-tuning arc expression upon BDNF signaling. Frontiers in molecular neuroscience, 11, 145.