Putting a gene in front of an inducible promoter, and then inducing that promoter is typically considered over-expression of a gene. Artificially inducing expression of a gene in a context in which it would normally not be expressed, and expressing it at higher levels than considered normal for that gene, would be considered over-expression of a gene (and is also up-regulation). However, up-regulation of a gene in its native context is not over-expression. There are myriad ways of measuring gene expression profiles, regardless of whether they are over-expressed. Like any gene expression measurement, you might have to calibrate your linear range across various orders of magnitude.