The Dairy Free diet is quite often confused with a vegan diet. As it is the same with Plant-Based diets
If someone follows a dairy free diet it is either out of choice, mainly for health reasons or they are allergic or intolerant to it.
A dairy product is a food that is made from milk. This will include milk products such as cheese, yoghurt, butter and cream. These products contain Lactose.
Lactose Intolerance
If an individual cannot tolerant milk and milk products, they are Lactose Intolerant. Lactose Intolerance is where the body cannot break down the Lactose in the stomach, an individual cannot produce enough of the enzyme Lactase to break down Lactose and digest it. Symptoms will include bloating, wind, diarrhoea and sickness.
If someone is Lactose Intolerant it means that they can have a small amount of Lactose. This condition is not life threatening it will cause a lot of discomfort.
People who are Lactose Intolerant will remove all milk products from their diet or replace them with Lactose free products for their milk equivalents. These products are not always vegan and may still contain animal products, they may still eat meat, eggs and honey as well.
Milk Allergies
A milk allergy is a reaction to the milk protein by the immune system. It can cause anaphylaxis where the tongue or throat swells and can cause shortness or lack of breath. This is quite life threatening and can happen very quickly and can take a few minutes if the correct action is not taken.
The allergy can take more time to develop in babies with symptoms such diarrhoea, abdominal cramps, loose bloody stools, coughing, wheezing and many more.
Vegan Diet
A vegan diet is a diet out of choice for ethical, environmental and compassionate reasons
A vegan maybe Lactose Intolerant or choose a Dairy Free diet.
A vegan may also have a Milk Allergy
A lactose intolerant diet or milk allergy diet may not necessarily be a vegan diet but any one of these diets can be a vegan if the individual choses that pathway.
As you can see that there are many differences between a Dairy-Free or Milk Free Diet to a Vegan one. The main difference is whether the individual chooses to eat animal products or not.
Sources
http://www.nhs.uk/Conditions/lactose-intolerance/Pages/Introduction.aspx
https://en.wikipedia.org/wiki/Milk_allergy
http://www.mayoclinic.org/diseases-conditions/milk-allergy/basics/definition/con-20032147
Maryellen Edwards 
I’d never given much thought to the difference between lactose intolerance and milk allergy – your explanation is great! I had no idea one was so much more dangerous than the other.
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