In Baseball, is there a specific term for the team that bats second?

I am a big fan of baseball and I can't live without it.

Chasing team doesn't refer to a home team in baseball which doesn't have anything to chase. Each team has 9 innings and they usually (in Major League) can't score as many runs in baseball as in cricket especially when aces (the best pitchers in each team) pitch the ball.

Two advantages for a home team in batting in the bottom of each inning while a visiting (away) team bats in the top are (1) it can finish a game by batting only 8 innings if a visiting team doesn't lead a game and a game is not tied in the top of the 9th inning and (2) it could have a psychological advantage known as home advantage as explained in Wikipedia:

In baseball, there is always a psychological home advantage when the game is tied or close in the 9th or in extra innings. The visiting team, if they are leading after batting in their half of the inning (the top), must face and record three outs against the home team in order to finish off and win the game. But the home team, upon scoring the go-ahead run in the bottom of the 9th or an extra inning, wins in sudden death without having to take the field defensively following their period at bat. If the home team is in the lead following the top of the 9th, the game ends at this point, and the bottom of the 9th is not played at all. There is no clear-cut, physical advantage because both teams are given the same number of opportunities (i.e. innings). The advantage is knowing how well one must perform in the last inning, if at all.

There is no alternative word to replace home team in baseball. I heard a bottom inning team mentioned several times, but it is rarely used to mean a home team.

A tongue-in-cheek expression for the home team (which is really the only term in use) is the good guys, at least to fans of the home team.

There is not really a second half of a baseball game. Given that there are nine (or seven) innings, each game develops at its own pace, and it may take one hour to play the first five innings and then another hour to play the sixth inning. Football, soccer are sports whose games have first and second halves. In baseball there is the seventh inning stretch which marks a recognizable spot in the game.

There is a second, or bottom, half of each inning, except the last non-extra inning if the home team is ahead; or if a game, once started, gets called (cancelled) due to rain or something else and at least four and a half innings has been played and the home team ahead (there are some exceptions to this). In this sense, baseball recognizes a sort of halfway point.