gDNA = "genomic DNA" and cDNA = "complementary DNA." cDNA is classically associated with being reverse transcribed either from all extracted RNA from a tissue or cell (total RNA) including (in eukaryotes) pre-mRNA, ribosomal RNA, tRNA, snoRNA, miRNA and mRNA, etc.) while cDNA obtained only from reverse transcription of the mRNA (expressed eukaryotic cytosolic mRNA) fraction (e.g., by poly[dT]n and random priming) is complementary DNA (cDNA) made from what is called the "transcriptome." Eukaryotes have introns and exons in the gDNA, while prokaryotes do not. So eukaryotic cDNA reverse transcribed from mRNA lacks introns. Prokaryotic-derived cDNA is always complementary to prokaryotic RNA and gDNA (so is always necessary to have a good DNase treatment prior to gene expression analysis by e.g., qPCR for prokaryotic transcriptome work)...
It is also worth noting in eukaryotes that histones and ribosomal RNA transcripts do not contain 3' poly-A tails (and so would not be reverse-transcribed into cDNA when using just poly [dT]n priming).
If you are working with prokaryotes (which your question does not reveal; unless we are to always assume that 'plasmid work' is always associated with 'bacterial work') and your plasmid insert is successfully expressed as bacterial RNA/mRNA, then making cDNA should reveal whether or not your plasmid was integrated.
What is the difference between cDNA and genome DNA?. Available from: https://www.researchgate.net/post/What_is_the_difference_between_cDNA_and_genome_DNA [accessed Apr 12, 2017].