The difference is referring to the directionality of gene flow.
We talk about genetic introgression when there is some gene flow from one population (say, population A) to the other (say, population B). We would say that population A introgresses into population B. If gene flow goes both ways, then the two populations A and B are admixing.
From Wikipedia > introgression
> Introgression, also known as introgressive hybridization, in genetics is the movement of a gene (gene flow) from one species into the gene pool of another by the repeated backcrossing of an interspecific hybrid with one of its parent species.
From Wikipedia > Admixture
> Genetic admixture occurs when two or more previously isolated and genetically differentiated populations begin interbreeding.