Interquartile range

I'm having difficulty understanding how to interpret an IQR.

Is an IQR the amount of distance or range that the middle 50% of the data set can vary from the median? Similar to how the standard deviation is the typical amount of spread or distance each data point is from the mean?

For instance, say we are studying New York state resident incomes and found the median income is $25,200 and the IQR is $38,000. Does this mean that a data point from the middle 50% can vary from the median by up to $38,000 in either direction of the median? So, just like with the mean and standard deviation, we add and subtract the IQR from the median to get a range of -$12,800 and $63,200. Or, is it simply the possible range the middle 50% of the data can vary by? So, in this example, the spread of the middle 50% of the data can be up to $38,000.

I suspect the latter interpretation is correct since in the former case we end up with a negative boundary point that does not make sense in this context. However, if it is the latter interpretation, and the median is not being used as a point to add to and subtract from, then what would be the boundary values that the middle 50% of the data falls in between?