I could be wrong but I believe this is the relation.
TL;DR HapMap did SNP genotyping whereas 1kGP did whole genome sequencing, and some of the individuals overlap.
First we have to establish a distinction.
Genotyping vs Sequencing.
Genotyping is the capture of a persons genetic identity at a defined locus.
Sequencing is the capture of a persons "complete genome/segment of DNA" (https://www.biostars.org/p/5197/).
HapMap Phase 1:
Released 2005, consisted of genotyping (not WGS) of several million known SNPs in 269 individuals. It included trio (individual and their parents) genotyping of individuals from Yoruba (YRI), Utah (CEU), Beijing (CHB), and Tokyo (JPT).
HapMap Phase 2:
Released 2007. To increase the quality of Mapping ability the project had to identify more SNPs. Once they had several million more SNPs they conducted genotyping of the additional SNPs on the same populations.
HapMap Phase 3:
Released 2009. Was an effort to expand the populations mapped. Using the SNPs from phase 1 & 2 they genotyped (not WGS) individuals from 11 populations (7 additional).
1000 Genomes Project (1kGP):
Pilot released 2010. In an effort to make a more comprehensive map of human genetic variation sequencing (not genotyping) was carried out on 1029 individuals from 26 populations.
HERE is where the overlap is;
The 1kGP sought to make their data as useful as possible so they sequenced many individuals (but not all) from the HapMap project and some individuals from the ENCODE project.
Now in 2017 we have the beautiful Simons Genome Diversity Project (SGDP) and the Estonian Biocentre Human Genome Diversity Panel (EGDP) which both include more populations than the 1kGP and have better genomic coverage.
https://en.wikipedia.org/wiki/International_HapMap_Project
https://en.wikipedia.org/wiki/1000_Genomes_Project
https://en.wikipedia.org/wiki/Human_Genome_Project