Thisclose

'THIS CLOSE' is used in everyday speech, often accompanied by some kind of hand gesture, to describe how near to success, failure, disaster etc a particular project, person or whatever has come. You may hear someone say in the coming weeks that "England were this close to winning the World Cup."
The words can be used together in other contexts, but I have a feeling this is what you are referring to.
I do not know, off the top of my head, the answer to the second part of your question.

I don't think that there is a discrete term for typology that plays on the meaning of words, e.g., "I made a HUGE mistake!". One sees this used in advertising quite a bit, but the use of fanciful fonts or creative spacial arrangements is frowned on in formal usage.

Mike, I think you may have missed the point of Sara's question. She's not asking about the phrase "this close". She's asking about the typography of writing "thisclose" with no spaces between "this" and "close"; thus, they are this close together, a visual and contextual doublemeaning.