Cause of working on Allele-Specific expression, working I am trying to know more about expression quantitative trait loci (eQTLs). based on definition, eQTLs are loci that control the expression level of other genes by Cis or Trans effects. Transcription factors are also proteins (product of genes) that control expression level of other genes. So the question is that, are transcription factors some kind of eQTLs? (or eQTLs are some kind of TFs?)
No, eQTLs and transcption factor are very different things.
Like you described TFs are proteins that control the expression level of genes.
eQTLs are nothing that is physically present in the cell. An eQTL is the conceptual influence of an allele-specific DNA locus (a SNP) on the expression of a certain gene. Explained with an example this means that some with the allele AA has a different expression in 'gene 1' than someone with the allele TT. The eQTL does not even imply any causality, merely statistical association of the allele state with a change in gene expression. (Of course one possible causation for the change in gene expression is that the allele influences binding of a TF to that locus.)