Light rail is a fancy name for trolleys. Amtrak and the freight railroads are heavy rail.
It actually gets worse than that. Since there are passenger rail services divided between the Federal Transit Administration and Federal Railroad Administration (the latter over the “general railway network”), the classification of heavy (subways) and light (trolley) railways fall under the FTA’s jurisdiction, and apply to operations not on the FRA’s network.
Nowadays, the FTA is even differentiating “light rail” (trolleys that serve suburbs) and “streetcars”, e.g. the difference between the MAX and Portland Streetcar in Portland OR; the latter is far cheaper (at $10 million per mile versus MAX’s $60 million per mile for its first line, the Interstate MAX).