What is the difference between the meanings of ball point figure and ball park figure?

Answer 1

The English idiom is 'ball-park figure', which means an approximation, or rough guide.
The expression 'ballpoint figure' is not shown as an English idiom in any standard reference work. (See notes)

'Ball-park' in the expression 'ball-park figure' means that the amount is within a range the size of a ball-park!* But this is not to be taken literally! It is just an idiomatic phrase with it's own unique meaning.

For example, if someone wants to buy a house, and has a large budget, and could spend, say, up to 400,000 dollars, but would be very happy if they could buy a suitable home for, maybe 200,000 dollars, then, if the real estate agent says,
"What price properties are you interested in?" their reply could be
"Well, it all depends on what's available, but, at this stage, my ball-park figure is around 300,000 dollars."

In this example the range is some 200,00 dollars between top and bottom.
Of course, a ball-park figure can have a much smaller range, depending on the subject being discussed and the degree of precision the speaker wishes to provide or indicate (or not!) to the other person.

NOTES
1. *a 'ball-park' is American English for a field for playing Baseball with seats for spectators. The use of 'ball-park' in a figurative sense to mean 'an approximation within an acceptable range' first appeared in 1960. It was used to indicate the area in which a returning spacecraft was expected to land. i.e. a largish area, but within reasonably approximated limits.

2. 'ball-point figure': It is possible that someone inadvertently said 'ball-point' when meaning to say 'ball-park.' Or that this phrase was/is used by someone not too familiar with the English idiom 'ball-park figure' or its origins.

Interestingly, one of the earliest appearances in print of the phrase 'ballpoint figure' being used to mean 'a rough approximation' was in a newspaper column/article in 2004. 'Ball-point figure' was given as an example of typical expressions uttered by 'haggling hillbillies' (Ref: Business Standard newspaper, New Delhi, India, September 11, 2004)

One dictionary says of 'hillbilly' that the word is "Often Disparaging and Offensive" and that it means "a person from a backwoods or other remote area", thus implying that they are uneducated and ill-informed.
For more information, see Related links below.