An operon is a sequence of genes under the control of a common promoter, e.g. the lac operon in Escherischia coli, transcribed and translated either as one common polycistronic string of mRNA or (in the rarer eukaryotic operons) “chopped up” into monocistronic mRNA molecules, either way the operon expresses either all of the gene products it codes for or none at all.
From an evolutionary point of view, an operon allows a prokaryote to rapidly produce a particular metabolic toolkit (e.g. the lac operon encodes for an enzyme which cleaves lactose, an integral membrane protein which promotes the active transport of lactose into the cell and an enzyme which renders toxic metabolic byproducts inert) all complete as and when required to take advantage of the sudden availability of nutrients in a rapidly-changing environment without wasting nucleotides and energy on maintaining a stock of them at all times.
An ORF is the region from one start codon (ATG) up to but not inclusive of the following stop codon. It’s rather more complicated with eukaryotes as we have introns to worry about, which may contain a stop codon, so the eukaryotic ORF refers to the complete exon sequence of a length of post-splicing mRNA between an AUG and an exon stop codon.
So an operon is a prokaryotic sequence of discrete ORFs with a polycistronic product (there are stop codons between them but no transcription terminators), the monocistronic ORFs of a eukaryotic cell are not commonly arranged into operons. The few eukaryotic operons have their polycistronic product chopped up into monocistronic mRNA post-transcription.
Warning -- this is a basic look by a beginner below your level! I would suggest looking up e.g. the 6 open reading frames of a particular strand of eukaryotic DNA and approaching a professor for any more serious questions.