It's the position in the protein.
p.Arg452Pro means that there is a variant that changes an Arginine residue at position 452 of the protein into a Proline.
And yes, it is absolutely possible to have the same HGVS p. notation on the same gene but on different transcripts. More than possible, it is quite common. Your particular example isn't actually a real variant since that position on chromosome 4 is intronic in both hg19 and hg38, but TP53:p.R175L1 is a real example of what you describe:
As you can see in the image or by visiting the link, this variant on TP53 has the same HGVS p. notation on 6 transcripts. It also has a different p. notation on two more transcripts that are not shown in the image as well as no p. notation for a few other transcripts in which it doesn't affect the protein product.
1Disclaimer: The link goes to https://varsome.com, a free human variant search engine that is developed by the company I work for.