In fact Vrat and fast are two different but inter-related terms. Vrat means to take vow or make a resolution. This vow can be of any kind, such as "I will speak truth", "I will not eat sugar for one month", "I will lose 10 ponds weight in two months time" etc etc. While fasting means "Upavaas" or not eating in a certain fashion. Thus Vrat is a broader term whose one part is fasting, because when one keeps fast, he takes a vow that he will not food till evening, or night, or the whole day etc etc; but Upavaas or fasting is the narrower term under Vrat and is used normally for the abstinence of food only.

Upavaas or fasts is not an indigenous term for Hindu religion, it is also common to other religions - Christians keep fast in their Lent days; Muslim keep fasts in their Ramaadaan days, Jain also keep many fasts, sometimes 3-day long fast. What is the point of this fasting in all religions? Fasting is deep rooted with the concept of Tapasyaa. Perhaps Tapasyaa is not complete without fasting. We have several instances of fasting in our scriptures, such as Paarvatee Jee kept fast for several thousand years to get Shiv as her husband. Why is it so? Because food is the third most important thing for life, after air and water. That is why when we want to appease somebody we leave food, so that to whom we want to appease he should know that we are not taking some important thing for our life.

Many Types of Fasts
Upavaas (fast) are of many types. In any type of fast, one takes the vow not to eat anything for certain time. If somebody cannot keep fast for the whole day, he is allowed to take juice or sweets to be taken only once and then eat the normal food at the prescribed time. Some common type of fasts are :--

(1) In some fasts only one type of thing is eaten or not eaten, such as on Tuesday, which is the fast for Hanumaan Jee, people eat only once in the evening and do not eat salt. In the same way in Thursday fast, people do not eat for the whole day and eat only yellow color thing once in the evening, besides they hear the Thursday Kathaa (story) also in the morning.

(2) Some fasts are kept for the whole day without drinking water, such as Nir-Jalaa Ekaadashee, Karavaa Chauth, Hoyee Ashtamee - these fasts are kept normally without drinking water, but in most fasts, water is allowed.

(3) In some fasts, Ann (cereals and grains) are not allowed to be eaten the whole day. One can eat only once that also fruits and roots etc. There is a cereal called Kuttoo (buckwheat), which doesn't come under cereal, can be eaten on that day. It can be ground as a flour and breads can be cooked out of that.

(4) In some fasts, people eat only after seeing Moon or star, such as Poornmaasee Vrat, Karavaa Chauth Vrat, Hoyee Vrat, Sankathaaraa Chauth Vrat.

Naarad Jee said - "You have asked a good question Ambareesh. Bhagavaan, if worshipped with Bhakti, gives all kinds of desired things. Ahinsaa, Satya, Asteya (not stealing), and living without cheating - these are called mental Vrat. Eating once a day, not eating in the night and eating only that food which is got without asking - these are told Kaayik (physical) Vrat for men. Studying Ved, Keertan of Vishnu's name and Leelaa, speaking Truth, and not telling about anybody to anybody else - these are called Vaanik (speech related) Vrat. Keertan cleanses everything.
[Padm Puraan, 4/19]
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Then, options are given for those, who for some unfortunate reason cannot complete certain vows. If one cannot bathe in water, he should bathe with the names of Vishnu. If one cannot follow the directions for completing a vow, one may complete it by feeding Braahman. If one cannot offer a lamp, he should light the lamps of others or protect their lamps from the wind and so forth. If no Tulasee is available, one should worship a twice-born Vaishnav. In his absence, one should serve Braahman, cows, Bodhi-trees and banyan trees.