Rather than using a reference genome, as in STAR, Kallisto uses transcriptome quantification for pseudoalignment, which means that it studies the amount of RNA transcripts produced to match sequences to a de Bruijn Graph without having to actually match the sequence to the reference genome. Kallisto takes 1/4 of the time STAR takes to run and uses about 1/7 of the storage.
References:
Bray, N., Pimentel, H., Melsted, P. et al. Near-optimal probabilistic RNA-seq quantification. Nat Biotechnol 34, 525–527 (2016). https://doi.org/10.1038/nbt.3519