Should I say "more exact"/"more precise"?
Solution 1:
You can have more and less accurate. It is the closeness to a target. Rifle shooters are awarded points in order of accuracy to the bulls'eye. The accuracy of the description from the eyewitness with bad eyesight, was very low.
Precise relates to very fine detail - how carefully measured (or described) something is. You can be precise and not accurate. I have two watches. One with only hours minutes, but the other gives seconds also, so more precise measuring of time. ( I wish it was digital and even more precise to 0.1 seconds measurement). Anyway, I missed my 9:00am train every morning for a week using the more precise watch! How ? Every day I arrived at the train platform very precisely at 8:54:49 (+/- 1 second) - repeatedly - I am very measured! However, I kept missing the train! Why? Well because the time on the watch had not been set accurately - it was 15 minutes out from the true time - inaccurate. I was measuring precisely ( to the nearest second) but was not at all accurate in my time measurement. Precise but not accurate. A person can give a precise (detailed ) description of a location (bench, path, fence, gate , tree, rock, etc) - but be totally inaccurate to the actual location (on a map say, or street name in a town) of an event.
"I am writing a blog that has a title "Love and Lust". I want to point out that it is more accurate/precise to say that the title should be "Romantic Love and Lust", as there are three kinds of love."
Perhaps the words you want are less ambiguous (more defined, more clear):
I want to point out that it is less ambiguous to say that the title should be "Romantic Love and Lust", as there are three kinds of love.
Otherwise I think I would go with both - precise (more detailed description) and accurate :
I want to point out that it is more precise, and accurate, to say that the title should be "Romantic Love and Lust", as there are three kinds of love.
Solution 2:
Both "precision" and "accuracy" are measured along a gradient of success. This is usually refereed to as the "degree of accuracy" or "degree of precision." When referring to a specific instrument, the measurement should be contextually obvious:
This ruler is accurate within one millimeter.
This cannon is so precise I can hit a target from one thousand yards.
"Precision" and "accuracy" are also contrasted with the word "error":
The margin of error for this thermometer is 0.001 degrees.
This means that neither word necessarily imply absolutes. When supplied without a specific qualification the details are either assumed via context or are not relevant for in this particular context.
This bow and arrow is precise.
You can easily add subjective qualifiers to this usage or even add an absolute qualifier:
This bow and arrow is [extremely/very] precise.
This bow and arrow is perfectly precise.
The word "exact" is different in that it implies an absolute.
What were their exact words?
I need these measurements to be exact.
But the concept of a "margin of error" is still implied because the real world doesn't appreciate absolutes. If you want exact measurements you still need to stop at a certain level of precision. The following conversation still makes sense:
I need these measurements to be exact.
How precise?
Within one millimeter.
Amusingly, this also means the question, "How exact?" has an immediately understandable meaning given the appropriate context.
In the end, neither "accurate" nor "precise" necessarily imply an absolute. "Exact" does imply an absolute but only in a philosophical sense. If you are using the word "exact" to describe reality then it is perfectly acceptable to ask for an acceptable degree of accuracy or margin of error (unless it actually is feasible to achieve a perfect result.)
As for your second question, there is a subtle difference between "accuracy" and "precision" when used within a scientific context. Wikipedia has an entire article on the topic. Here is their quick overview of the distinction:
Accuracy is the proximity of measurement results to the true value; precision, the repeatability, or reproducibility of the measurement.
In other words, "accuracy" refers to how well you did and "precision" refers to how differently each of your attempts were. A specific example: If you threw three darts at a dartboard and they all landed next to each other then your throwing arm was precise. If they landed near the bullseye then your throwing arm was accurate.
Colloquially, there is no distinction between the two.