Munich to Berlin

How about bus?
https://global.flixbus.com/

It's 360 miles between the two cities and about a 4:35 hour train ride on ICE. I'm seeing fares running $75 to $100 for trains in the coming week one way--very reasonable. The train might be faster than flying when you consider all the sitting around and going to/from the airport.

is this from the DB site?

How many people and what day? If you are looking at Easyjet, be sure to factor in cost of hold luggage, seat selection, transport to and from airports.

Definitely check on bahn.com, if you have your information from another website. A $250 difference sounds strange, as the walk-up fare is only around 150 Euros for the train (price for one person, varies slightly depending on the day of the week). Even for the fast connection (under 4 hours), tomorrow morning, there is a saver fare of 130 Euros available.
Having said that, there is nothing really wrong with flying. Munich airport is far outside the city, but Tegel is not; so overall, the journey time will be about the same. Of course, a direct train from city centre to city centre is more convenient than the multiple stations of a journey by plane (getting to/from airport, security, ...).

Sandy - Did you try airlines such as Easy Jet and Ryanair, Wizz Air, and Wow Air to fly from Munich to Berlin ?

perhaps the airfare will be cheaper

There are 3 of us traveling and I'm looking at the direct trains. We are flying into Munch from the States and heading straight to Berlin for the first few days of our trip and then returning to Munich. Eurowings is like $235 RT for all 3 but we will be hanging at the airport for a few hours...OR, I can pay the $520 RT for us and spend the day in Munich and catch the train to Berlin in the late afternoon. I'm really leaning towards spending the extra money for the train.

You still have not said what day you are arriving at Munich airport.
I see a few Sparpreis tickets for 317.70 EUR for 3 (~$356) everyday for the next few days, then prices drop beginning Monday.

First, are your Eurowings flights flexible? At the price you mentioned, they sound like nonrefundable tickets to me. Just like Sparpreis tickets, they could be completely worthless if you are severely delayed.

Here is a modest proposal. You could buy German Rail Passes. If you have time to get the passes expressed mailed to you, 1 Adult and 1 Twin 3-day Flex GRP would be 492 EUR (~$552), just a little more than what you would pay for 3 Flexpreis tickets from Munich to Berlin, and you would also be covered on the return trip to Munich.

If you don't have time for this, you can buy consecutive passes on-line. 1 Adult and 1 Twin 5-day consecutive GRP would cost 550 EUR (~$616) and the 5 day would cover you for the return. Or maybe 4-day would work at 520 EUR. You can print these on-line.

With German Rail Pass, you can take any trains you want without having to worry about making a specific train.

If one of your traveling companions is 12 to 27 yo, You could spend less and buy 1 Twin and 1 Youth GRP, 452 EUR for the 3-day Flex, for instance.

I'm sorry Sam, we will be arriving in Munich on Friday, June 7th.

You have plenty of time then. Must be getting to the Summer travel season, even Flexpreis tickets are higher. Consider what I said about German Rail Passes. Added flexibility, you can still take any train after you arrive and don't have to worry about loosing Sparpreis tickets due to late arrival or wait extra time as a safety factor, and use them for other trips like your return to Munich. I was just clicking through on the Rick Steves link to Rail Europe and I got $506 for 1 Youth and 1 Twin 3-day Flex GRP's. Leaving June 6, there is plenty of time to have them mailed to you.
For you arrival day, it looks busy, so spend 13.50 EUR to get 3 seat reservations.

Friday June 7 is the lead in to a 3-day German holiday weekend. Monday June 10 is Whit Monday (Pfingstmontag), So now you know why Friday train prices are high.

To save a lot of money but lose a lot of time there would be a Quer durchs Land ticket that would take 9 hours to get from Munich to Berlin with 3 changes, but only costs 60 euros total for 3.

On the flying option between Munich and Berlin...I would not advise that, certainly would not do it myself, wouldn't think of it. Take the ICE train, some are direct connections.

This is your plan? Sit on a plane for 8-10 hours, then sit on a train for another 6 hours, adding in your time you will spend waiting for this train? Seriously? How exhausted will you be once you get to Berlin?

Stay overnight in Munich, sightsee, have a nice dinner, go to bed a bit early and catch one of those early morning trains to Berlin. You may even find better prices. You also don't have to stress about delayed flights and can enjoy that train ride the next day, seeing the countryside and not worry about falling asleep on the train.