GWAS terminology "Tag" vs "Lead" vs "Index" SNP
I found a review paper that addresses your questions, see 

Schaid, Chen, Larson (2018): From genome-wide associations to candidate causal variants by statistical fine-mapping

Tag SNP. You correctly identified tag SNPs. From the paper:


  [T]he SNPs on microarrays, called tag SNPs...


Lead and index SNP. These are apparantly synonyms. From the paper:


  This allows one to focus on the SNPs with the smallest
  (that is, most significant) P values in distinct regions,
  sometimes called the lead or index SNPs.