Amsterdam to Rotterdam. By train

If you use the ns.nl website, you can tell by the way the trains are depicted in the left panel whether there will be a transfer (you'll see two different train icons). If you click on a particular departure, more details will appear in the right panel (if you're using a PC).

As long as you stay off the $$$ Eurostar, you don't need to make a reservation; tapping in and out is fine.

If you're willing to commit to departure timing by buying your ticket a few days ahead of time, check the schedule and look for departures labeled "PriceTime deal". I'm seeing some opportunities to save about 5 euros on Thursday. There are larger discounts for trains departing 2 or 3 weeks from now. (The regular fare is about 20 euros.) Those discounts are triggered by slow ticket sales, I think, so you won't see them now for May departures. Click through on one of the trains flagged as offering a PriceTime deal and the next screen will show you the validity period for the ticket, which may be several hours long.

Don't know which place you were using but the best website to look up is www.ns.nl.

Almost all domestic trains in the Netherlands can be paid for by tapping in and out with a credit card, if the card is generally accepted for contactless in Europe. A few journeys listed as "Intercity Direct" require a supplement (pay online or tap in at a specific terminal) but they don't seem to be the continuous ones from Amsterdam Centraal to Rotterdam. You can tell if a train is continuous or if you need to change quickly on the website by looking at the number of little train icons beneath each journey on the result list. The site also shows in green for each journey if you can potentially get a discount by booking in advance rather than using contactless.

Thanks for the extra information. I was looking at the correct website but didn't know to look for 1-2 little trains. I had noticed that there was a reference to a supplemental fee on some of the intercity trains - but was worried about how and where to pay that and thought that might involve changing trains (which we prefer not to do).

I was using a table originally but will look at the website on the PC and look for the additional details. Appreciate the assistance
Mary

The Intercity Direct trains with the supplement (just means, slightly more expensive) are the ones using the High Speed tracks between Schiphol and Rotterdam - so they are faster and don't stop much.

If the others, which will stop at least several times, are fast enough for you you don't need to use the high speed line.

As always, your choice.

The Dutch railway system is basically a nationwide subway, and you should treat it as such. Going from Amsterdam to Rotterdam is as trivial as going from Brooklyn to Manhattan.
So just go to the station, and tap in/out.

The only thing to watch out for is that there is a supplement for the "Intercity Direct" services that take the fast route. If you want to board these trains you have to tap a second time at a special totem on the platform to pay the supplement. This is clearly indicated.

However all the ICD trains go from Amsterdam Zuid nowadays. If you want to leave from Amsterdam Centraal, and want to have a single seat ride you will be on an IC service via the old route anyway.

There is a map of the whole NS train network here:
https://nieuws.ns.nl/download/8dd1a03e-ae92-4f51-99c7-928eb91b2b4d/spoorkaart2026.pdf

Every line means a train per half hour. You will notice that if you don't mind changing you have a train every 10 minutes, but if you want a direct, single seat ride you still have as train every half hour. Look for the trains with final destination "Vlissingen".