In cafes the person who prepares the coffees (and sometimes alcoholic drinks) is called a barista, from the Italian.
I've only heard the term being used relatively recently in Ireland but I have seen loads of ads in windows saying "Barista required".
Being a barista can often suggest that you have a professional training in the art of making coffees.
I don't know about European cafes, but in American restaurants that serve alcoholic beverages with meals, there is often a bar area (physically sequestered but part of the establishment), with a completely different ambience-- smoking allowed, TVs on, gambling and video games along the walls, perhaps a pool table and even a bandstand and dancefloor.
You can order your meals from the bar, in which case a waitress will serve your food there-- I use the gender-specific form because "barmaid" is the topic of the thread.
If you eat at the bar, you'll be kept in drinks by the bartender, but she will also be in charge of any barmaids who haul them by the trayful to the tables/booths in the bar.
If these barmaids serve restaurant patrons, they are called runners, or drink runners-- not barmaids, I guess, because they are functioning outside the bar.
One caveat, if they keep a running tab for the drinks, please don't leave a single tip on the table and assume the waitress will "tip out" to the runner, any more than she will the busboy or the cook. In some restaurants, that is done-- in which case you'll receive a single bill from your food server, with the drink subtotal included.
In my part of the country you can certainly call for the barmaid just as you would the waitress, but I spent my gradschool years in a city elsewhere, where the word was considered a little demeaning. Barmaids were called bartenders whether they worked behind the bar or ran drinks.