When Americans speak of expert and master, they’re referring to a rating of their playing level according to the United States Chess Federation (USCF). Not sure what the situation is in Europe, there’s FIDE, Federation International something or other chess.
Almost all tournaments in the US are USCF rated. A player entering a tournament is given a provisional rating at first depending on the level of player he/she wins against in tournament play. After twenty games or so, they recieve their regular rating. Winning or drawing against someone of a higher rating causes the player to gain points- they lose points if they lose or draw against a lower-rated opponent. The only criteria for entering an open tournament (as opposed to a closed, “by invite only” one) is to pay the entry fee(s). I say fees because it is usually always a requirement to join the USCF, and the state’s chess group, as well.
Regular tournament players are stronger, usually, than casual players. They play more, they study more, and they play against stronger players. In my old now-defunct chess club, we used to have kids come in quite often who had (usually) learned to play recently, caught on quickly, proceeded to beat the tar out of all their family members, and acquired an ego about it. (I’m not speaking of your brother here, just of my experience.) We always sent the new kids to play the old guy.
The old guy was a lovely gentleman of about 90 or so, who had trouble seeing the board clearly despite enormous thick glasses, and couldn’t hear too well, either, despite the hearing aid, and had to touch the pieces often during the game because he tended to confuse the bishops with the pawns- and he would whup their asses, individually and collectively, every time. You could see the little egos deflating by the minute.
He actually had a pretty solid game, was probably about 1400-1500 rated, and had been playing since his college days (yep, 70+ years). But these kids- heh, thinking they were hotshots till they faced the old guy. We privately called it “Weeding out the Weaklings” because if you go to clubs or play in tournaments, you’re going to lose a lot before you start winning, and if you can’t deal with losing (particularly against a guy who can barely see the board) you probably don’t have the fortitude to stay with it. As they say- chess is easy to learn, difficult to master.
Thought I’m not a kid, it took me 6 months to beat the old guy. He sure was proud of me when I finally won. 
One more thing and I’ll shut down this ramble- if you’re a single woman, playing chess tournaments is a great way to meet guys. I got asked out all the time when I used to play, and was single.