According to my friend, there is a difference between “food” and “rice”. Well, for her every other thing we eat with rice is “food”, and rice is just rice for her. For example, If we eat chicken and rice, then she calls chicken as food.
Is your friend a native speaker of English? I suspect she might be mapping words from another language onto English. (Rarely is there ever a perfect fit.)
In East Asia, for example, rice is the most important staple, and in most areas some kind of rice or rice product is eaten with almost every meal. It is so central that the Chinese character 飯 indicating cooked rice can also mean food or meal in general, in Japanese as well as Chinese use. In Korean 밥먹자! (bab meokja!) translates literally as "let's eat the cooked rice!" but ordinarily just means "let's have something to eat!" or "let's dig in!"—even if you are having goulash or tacos.
The point is that historically, if you asked someone what she was going to have for dinner, she would never have answered "rice"— that would have been taken for granted. I have older Korean relatives who to this day will chuckle if I tell them I had rice— well, obviously. When they ask me what I had for dinner, they want to know what meat, stew, and 반찬 (banchan, side dishes) I had. This seems to correspond to the distinction your friend is making between the staple/core of the meal and its accompaniment.
None of this applies in English, however; in standard usage, the distinction your friend makes does not exist. Rice is simply one type of food. Declaring that food only refers to foods other than rice is unsupported either by common usage or by dictionaries. I do not know if her use is common, but anecdotally speaking, none of the people I know who might refer generically to food or a meal or a dish as 飯 or 밥 in another language ever use rice in that way in English.
Bread is the nearest Western equivalent. We still have many expressions involving bread in English, like breaking bread (sharing a meal) with someone, something being your bread and butter (essential or basic), or knowing which side your bread is buttered on (recognizing a benefactor or source of advantage). Still, I do not think bread ever attained the cultural centrality in the English-speaking world that rice did in southern and eastern Asia, and I have never come across anyone who would try to declare that bread was in a special class of edibles. Bread is food, just like everything else you eat.
Is your friend a native English speaker? It's possible that that is how it works in another language she speaks and she has transferred that construct into her English. In a way, I understand what she is trying to say i.e she wouldn't eat just rice as a meal and it's more of a complement to the more important/enjoyable parts of the meal e.g chicken, some other type of meat, etc. Where I grew up, the veggie sauce and meat were considered the most important parts of the meal and I assume she has also grown up with similar ideas.
Regarding your question about whether food and rice are different, your friend is wrong and rice is definitely a type of food.
The OP's friend might be thinking of starchy foods (today more commonly known as foods high in carbohydrates, carbs) compared to other types of food. She probably considers that "rice" = filling, but "food" = nutrition/taste.
Starchy foods include bread, pasta, rice, couscous, potatoes, breakfast cereals, oats and other grains like rye and barley. Although these starchy foods are often referred to as 'carbs', this is a little misleading as carbohydrates include both starch and sugars, as well as fibre.
Maybe she is thinking that rice, potatoes and bread alone are not meals by her standards. But the terms meal (breakfast, lunch or dinner) and food have distinct meanings.