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.