Types of Romance Fraud

What is it?
fraud
/frɔːd/noun:
wrongful or criminal deception intended to result in financial or personal gain.

“he was convicted of fraud”

a person or thing intended to deceive others, typically by unjustifiably claiming or being credited with accomplishments or qualities.
“mediums exposed as tricksters and frauds”
romance
/rə(ʊ)ˈmans,ˈrəʊmans/noun:

“I had a thirst for romance”

verb:
try to gain the love of; court.
“the wealthy estate owner romanced her”
Romance Fraud is the intended use of a created fake romantic connection as the deception to commit fraud. 
In some Romance Fraud, false representation applies to identity as well as intent.
Fraud legislation in the UK.
A person is guilty of fraud if he is in breach of any of the sections listed in subsection (2) (which provide for different ways of committing the offence)
Romance Fraud comes on a huge spectrum, with many scenarios to fit under the description.
The common thread with all of them is the manipulation victims are put through which is Adult Grooming, to make them compliant to whatever the intent of the connection is. You can read about this manipulation here.

More information can be found on the individual pages for each type of romance fraud.