An inducible operon is the one in which transcription is usually off. Transcription gets initiated as soon as inducer enters the cell. For example, lac operon. The genes of lac operon are catabolizing genes.
A repressor operon is the one in which transcription is usually on. But, transcription switches off as soon as a co-repressor binds the repressor. For example, tryptophan operon. The genes of tryptophan operon are biosynthetic genes.