Sequences with identical descriptions but different lengths are likely orthologs from different species.
You can filter them by sequence identity using CD-HIT. If you select a 90% identity cutoff, it will cluster together all the sequences that share 90+% identity, and keep a single (and longest) sequence from that cluster. That will likely take care of your partial sequences without having to grep them out.
It is up to you to select whatever identity threshold makes most sense. More sequences will be retained at higher cutoffs.
Different proteins (IDs) with the same description is not uncommon (more common than uncommon even). These are part of the same gene family. In eukaryotes, especially higher eukaryotes, this is a very likely scenario (gene duplication etc will increase the number of genes) , they have many paralogs (== genes with often similar/identical function) in their genomes.
Well, there is no choosing possible. They are all real genes with that function, none of them is more likely than the next one to perform that biological function