Welcome to the board, and welcome to the process of learning to read labels.
The Milky Way bar contains gluten (barley malt), and is not safe for us.
Gluten, defined in terms of celiac disease, is a protein found in three grains: wheat, rye and barley. Oats are generally contaminated with wheat, and a minority of us also react to pure oats.
The list of top allergens that must be disclosed includes wheat, but not the other three.
"Contains" and "May Contain" are different animals, too.
In the US, if a top-eight allergen is present, it must be listed by its common name, EITHER in the ingredients list OR in a contains statement. Only allergens may be listed in the contains statement. The eight allergens under the federal Food Allergen Labeling and Consumer Protection Act (FALCPA) are: wheat, soy, milk, peanuts, eggs, tree nuts, fish, and crustacean shellfish. Since barley and rye are not on that list, they will never appear in a "contains" statement. (In Canada, the list also includes sulfites and sesame seeds.)
If there is a "contains" statement, it must list every allergen present. But, again, barley and rye are NOT "allergens" as defined by the label regulations.
In this example, barley was listed in the ingredients by name. As someone new to this, I understand your confusion. But the label is not misleading, and conforms to the rules. You can not rely solely on the "Contains" statement to identify gluten. You'll know about wheat, but not barley or rye.
Rye is not something you need to worry about. It is in very few foods, and those are confined to selected baked goods where you would expect it, like rye bread and pumpernickel. In my experience, it is always clearly listed on the label.
"May contain" means that the ingredient is not intentionally present, but despite Good Manufacturing Practices and other precautions, it is not possible to be sure that trace contamination does not occur. Like the previous discussion, only ingredients legally described as allergens will be listed.
And, last, a list of companies that has a clear gluten policy. If you don't see "wheat, rye, barley, barley malt, oats" on the labels, its not there, or hidden in "flavors, starches, etc." This makes shopping MUCH easier.
Edit: Three other posts were made while I was composing this.
Source: Could The Milky Way Ingredients Have Been Misleading?