tl,dr : It's a tournament. Tie = Match
The Capital One Cup (League Cup) is a single-elimination competition open to all clubs in the Football League (i.e. Premier League, League Championship, League 1 and League 2). Premier League Clubs are entered into the second round of the tournament and clubs with European competitions in the current season enter in round three (or, later?). The final is played at Wembly Stadium.
In the Queen's English, a "tie" is a match in cup/elimination scenarios. e.g. The Seattle Sounders are going to PPL Park for what is lining up to be a classic US Open Cup tie against the Philadelphia Union.
It's a bit confusing to American sports fans at first because we are accustomed to a regular and post season format. Most European leagues have their league and elimination/cup competitions held during overlapping schedules (with breaks in league play, or strategically-scheduled weekday games to avoid scheduling conflicts).
Other terms to know:
Replay - if a match ends in a draw for certain cup competitions, there will be no extra time, but rather a complete 90 minute rematch at the away-team's stadium.
Draw - for most domestic cup competitions (E.g. League Cup, FA Cup), opponents for each round are drawn out of a lottery. There may be some kind of regional element to it - but I'm not really sure. It could be 100% random for all I know.
Two-Legged Tie (Aggregate Score) - The semi-finals of the League Cup (and similar knock-out rounds of other competitions like the Champions League) take place over two full 90-minute matches. The score of the first match rolls over to the second match. Essentially it is a 180 minute game played at both teams' home stadiums. Some tournaments (Champions League, this year's MLS Cup) apply the 'away-goals rule' to determine the winner in the case of an even scoreline (can't say tie or draw
Away-Goals Rule - (My least favorite Soccer rule) - The victor in a two-legged tie will be determined, in the case the score line is equal, by the team with the greater number of goals on their away leg. E.g. Game One: NYCFC 1 - 1RBNY (at Yankee Stadium), Game Two: NYCFC 2 - 2 RBNY (at Red Bull Arena), NYCFC would move on to the next round because we have two away goals, while that team from Jersey has only one.