If I’m interpreting your location correctly, Northern Piper, you’re Canadian. Or, more relevant here, North American; most of the sports that dominate the market here have somewhat similar approaches to timekeeping, substitution, and player ejections that soccer does not share. Hence the frequent confusion.
As others have said, a yellow card is a formal warning for unsporting conduct (which includes but is by no means limited to excessively rough play). A red card is an ejection; it may stem from a single serious violation, but is also an automatic consequence of a second yellow card within the same game.
Red cards or accumulated yellows across multiple matches usually result in suspensions from subsequent games, but the details of this are left up to the particular league or tournament in question (the Laws of the Game are silent on this).
When a player is red-carded from a soccer game, he may not be replaced on the field. This is completely different from ejections in football, baseball, basketball, and hockey, and is a frequent source of confusion among North American viewers.
Soccer allows much more limited substitution than the Big Four North American sports. Of those four, only baseball stipulates that a player may not return after leaving the game, and all four allow full use of a roster of players more than double the size of the on-field contingent. Hockey even allows substitution while the puck is live.
In World Cup soccer, a team may use only three(?) substitutes; once they’re used up that’s it. Even if a player is injured and unable to continue, his team must play a man short. As in baseball, once a player is substituted out he may not return to the game.
Baseball is untimed, of course, but in football, basketball and hockey the official time is kept on the scoreboard clock; when it hits 0:00 the period is over. Soccer, not so much. Official time is kept on the field by the referee, and the stadium clock simply counts upwards from 0:00 without stopping. If there’s a delay in the proceedings (injury, etc.) the referee will effectively stop his own watch while things are sorted out. This means that the half will almost always extend beyond 45:00 on the scoreboard clock; this additional play is referred to as “stoppage time.”
“Extra time,” as you can see, has a very specific meaning in soccer and stands for something else. Specifially, it’s what a North American sports fan would generically think of as “overtime,” although soccer doesn’t call it that. Depending on the rules of the league or tournament, a soccer game may be called a draw if the score is tied at the end of the second half, or they may play extra time.