There are differences between test Karl Fisher test methods, and TAN and TBN methods. They all are there to give you the result at the sensitivity you are looking for. For example, one Karl Fisher method reports water concentration down to 10 ppm, while another’ minimal reporting limit is 0.05% (500 ppm). As far as titration methods such as TAN and TBN methods are concerned, one method is for clear and bright oils (manual titration), while another is for non-transparent, dark colored oils (potentiometric titration), where it is impossible to visually see the reaction’s end point.
If you don’t have access to test methods, talk to your lab personnel. Tell them the origin of your sample(s), how it visually looks like, what you want to test it for, and the level you are interested in. Based on such information, they would be able to suggest the method which would give you more accurate results in the expected range.