I'm trying to figure out the rules and any online explanations of scorecards don't match up with the abbreviated TV graphics.
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I've captioned each part of the scoreboard for you, below.
The answer posted above is good for the scorecard. There is also another scorecard that is a of the current score, plus other information, in a current game.
Very quickly, balls, strikes and outs are self explanatory. The image you see under the box "field" suggests the runners currently on the bases (in yellow). In the picture for example, there are runners currently on first and second base (first, second and third bases are counter clockwise in that order).
Finally, you have the runs scored per inning (up to 9 innings) unless there are extra innings in which it will go on to 10+ innings. Runs is the current score. Hits is the amount of hits each team has gotten, and err is the amount of errors the fielding team has committed.
In baseball games though, the runs, hits, and error category is usually abbreviated by R, H, E respectively.