TA - Travelling Allowance
DA - Dearness Allowance
The Travelling Allowance is the amount of money paid to an employee who went on a trip or a tour for company's benefit. Some organizations pay a flat amount of TA that gets added in the monthly salary. Others require you to show the bills of air ticket, hotel room bills, food expenses etc. and reimburses that amount with your monthly pay.
Organizations usually has a maximum cap for each entity like ticket, food, and accommodation charges. If you are eligible to travel via sleeper class you can't reimburse a flight ticket. The policies related to TA are defined by the company and could be changed anytime.
The Dearness Allowance is calculated as a percentage of the monthly basic salary or pension of an Individual. It is basically the 'cost of living' adjustment allowance that vary on the basis of the area in which one lives, i.e rural or urban.
The cost of living in Metros is obviously much more than in villages. So, a person working in some organization should be paid more than a person working in a village, in the same organization. This amount is adjusted with the help of DA.