what is the difference between local identity and global identity for homolog finding?
If you want a purely alignment based approach to begin to infer homology (note I say infer, as we stated in the comments, this isn't sufficient to say 2 sequences are homologs), I would use a Multiple Sequence Alignment (MSA) instead of a pairwise like you've done so far, and include as many similar proteins as you can from BLAST.

The choice of algorithm for the MSA probably won't matter too much, as you will be looking for conserved regions anyway.

Once you have your MSA, you can easily spot conserved domains. If anything is known about this protein structurally, it's quite trivial to work out whether a conserved region is a functional domain (active site, that kind of thing).

With this information, you would be somewhat justified in calling these proteins structural homologs at least if they share domains, but, to reiterate, without doing phylogenetic analyses, you cannot call them true homologs.