Different fare buckets for different levels of ticket flexibility. I always book the cheapest available on Amtrak since I am a semi frequent Amtrak passenger. If I need to change or cancel, I'll simply do that and roll the value from that fare into my account to use as a voucher for another trip.
If you are planning on travelling only once on Amtrak and "saver" fares are available, book that with the caution that you won't be getting $$$ refunded if you have to cancel. Changes are always permitted on Amtrak NEC (northeast corridor) provided seats are available. You may have to pay the fare difference.
In general NY-WAS has decent availability but Amtrak does price discriminate with fares on the more business friendly hours being higher than the off-peak hours. If you are flexible you can currently get from NYP to Washington for as low as $39.00 one way.