Identity By Descent vs Identity By State
The issue of IBD and IBS can indeed be confusing. 

The identity by state definition refers to the fact that at some point two individuals, even if they are not related to each other, present the same allele at a specific locus. Because of their un-relatedness this similarity probably arose from a similar mutational event.

On the other side, with IBD two individuals happen to share the same allele because of their coancestry. 

Alleles that are identical by descent are also identical by state. But the opposite is not true. (see also https://www.biostars.org/p/174048/#174049 and Powell et al 2010, Nature Reviews Genetics 11, 800–805 (1 November 2010) | doi:10.1038/nrg2865).

Now, about the threshold that you were mentioning in your question, I am not entirely sure what you mean. Eventually, all individuals are traceable to a MRCA (most recent common ancestor). So, I think the threshold you talk about refers to the size of the population in analysis. Depending on the size of your population you will have different proportions of alleles that are IBD and IBS. 

Hope this help.