The LOD definition is: the detection limit, lower limit of detection, or LOD (limit of detection), is the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) within a stated confidence limit (generally 1%). The detection limit is estimated from the mean of the blank, the standard deviation of the blank and some confidence factor. Another consideration that affects the detection limit is the accuracy of the model used to predict concentration from the raw analytical signal. It is a limit of the detection tool used.
The CUTOFF VALUE definition is: the cutoff (or cut-off) or cutoff value is a threshold value, maximum or minimum, is associated with a quantity, such as energy, or pulse length, and such that objects with values of these physical quantities above or below the cut-off are ignored. It is a choice of the researcher.
The LOD definition is: the detection limit, lower limit of detection, or LOD (limit of detection), is the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) within a stated confidence limit (generally 1%). The detection limit is estimated from the mean of the blank, the standard deviation of the blank and some confidence factor. Another consideration that affects the detection limit is the accuracy of the model used to predict concentration from the raw analytical signal. It is a limit of the detection tool used.
The CUTOFF VALUE definition is: the cutoff (or cut-off) or cutoff value is a threshold value, maximum or minimum, is associated with a quantity, such as energy, or pulse length, and such that objects with values of these physical quantities above or below the cut-off are ignored. It is a choice of the researcher.
Martino’s answers are very good, but I’ll try to explain something more about the cut off value: This is used in microbiology, immunology (ELISA, for example) and other quantitative diagnostic techniques to have a discriminant point between positive and negative results, you can calculate a cut off point doing different statistical procedures like ROC curves (Receiver Operating Characteristic curves), Youden index, with the mean and standard deviation of positive cases on a normal distribution, or applying linear mixed effect models.
There are different methods for calculating LODs and cutoff values. In clinical and forensic toxicology applications, LOD refers to the lowest analyte concentration measured in a sample that can be differentiated from a blank matrix. Cutoff or decision point is an arbitrary value established to identify a sample positive or negative for the target analyte. In terms of immunoassays, most are qualitative in nature, cutoff value can help an analyst identify a presumptive positive sample (for target analyte or analytes), and may require further confirmation to determine concentration. Cutoff optimization is critical for evaluating the immunoassay's performance. To optimize cutoff, typically you want to test the assay with samples fortified with your target analyte at concentrations (at least) +/- 50% of target cutoff. You also have to confirm these presumptive positive/negative samples by another method to determine immunoassay performance.
For further information, I recommend reading several method validation articles:
Araujo P, Key Aspects of Analytical Method Validation and Linearity