Primer is a small fragment of single-stranded DNA designed to bind specifically to one region in the genome to allow for accurate amplification of the diagnostic target area. Probes bind to the target area and emit a fluorescent signal as an indication of increased amplification in that area. This fluorescent signal is then read by a quantitative RT-PCR machine where a reaction occurs to provide a diagnostic reading. Molecular scientists use many different tools to design the most appropriate primer to create a functional diagnostic target.

Primer
Primer is a short DNA or RNA fragment that functions as an initiator for DNA synthesis. DNA polymerase enzyme adds nucleotides to the 3’ OH group of the primer sequence and synthesizes a new strand that complements the DNA template. Primers are very short fragments, typically 18 to 20 nucleotides long. They are chemically synthesized in the laboratory for in vitro DNA amplification (PCR). Primers can have any nucleotide sequence because they are designed by the user. They are synthesized to match the complementary base of the DNA template. Therefore, they can have any nucleotide sequence. Primers are crucial for DNA replication because DNA polymerase cannot synthesize new DNA without a pre-existing piece of DNA. When designing primers for PCR, the following factors need to be considered:

• Primers should contain nucleotides complementary to the flanking ends of the DNA to be amplified.
• Primers should have a melting temperature between 55 – 65°C.
• The annealing temperature should be 5°C below the melting temperature of each primer.
• G and C base composition should be between 35%-60%, with the ideal composition being 50%.

In PCR, two primers are used, the forward primer and the reverse primer, to replicate both strands of the sample DNA.

Source: https://commons.wikimedia.org/wiki/File:Polymerase_chain_reaction.svg?

Probe
Probe is a DNA or RNA fragment used to detect the presence of a specific DNA fragment in a sample. Therefore, probes can be used for two types of techniques, in qPCR and in hybridization reactions. Four things to consider when designing probes are:

• Location: Ideally, the probe should be near the forward or reverse primer, but should not overlap with the primer binding site on the same strand. Probes can be designed to bind to both target strands.
• Melting Temperature (Tm): Ideally, the probe should have a Tm 6-8°C higher than the primer. If the Tm is too low, the percentage of probe binding to the target will be low. In this case, the primer may amplify the product, but the low probe sensitivity results in decreased fluorescence signal, so it does not truly represent the actual amount of target present in the sample.
• Annealing Temperature (Ta): The annealing temperature should be set no more than 5°C below the lower primer Tm. Use this as a general guideline, but note that optimization may still be necessary.
• GC base composition: Like primer sequences, aim for a GC content of 35-65% and avoid G at the 5’ end to prevent quenching of the 5’ fluorophore.

Probes and primers are two types of single-stranded oligonucleotides used in various types of PCR. Probes are used to detect specific DNA fragments in qPCR. Primers are used to initiate DNA replication in cells and are also used in PCR initiation. Therefore, the main difference between probes and primers is their purpose.

References:

Difference Between Probe and Primer, https://pediaa.com/difference-between-probe-and-primer/
Designing PCR primers and probes, Integrated DNA Technologies