Regulatory health organizations have set various standards to control how much harmful or potentially harmful substances are allowable in the foods and beverages we consume.
Acceptable Daily Intake (ADI) is an estimate of the amount of a substance in food that can be ingested daily over a lifetime by humans without appreciable health risk. The concept of the ADI has been developed principally by the World Health Organization (WHO) and the UN's Food and Agriculture Organization (FAO) and is relevant to chemicals such as additives to foods, residues of pesticides, herbicides and veterinary drugs and hormones in foods.
ADIs are derived from laboratory toxicity data (and from human experiences of such chemicals when such is available) and they incorporate a safety factor. The ADI is thus an estimate of the amount of a substance in food that can be ingested over a lifetime by humans without significant risk to health.
Tolerable Daily Intake (TDI) is applied to chemical contaminants in food and drinking water. The presence of contaminants is unwanted and they have no useful function, differing from additives and residues where there is or was deliberate use resulting in their presence.
TDIs are calculated on the basis of laboratory toxicity data with the application of uncertainty factors. A TDI is therefore also an estimate of the amount of a substance (contaminant) in food or drinking water that can be ingested daily over a lifetime without a significant health risk.
Extensive tables of ADIs and TDIs are available at sites such as http://vm.cfsan.fda.gov/~dms/opa-edi.html
Most of the information in this writeup was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entries this is based on.