The previous one was also crewed (two crew) but it was called "demo" for some reason - despite taking astronauts to the ISS. How is the recent one different?
The contract between SpaceX and NASA required two demo flights (and SpaceX voluntarily did the in flight abort, notice Boeing is not doing that).
They did an unmanned demo flight with Dragon C201, that launched Mar 2, 2019 and docked to the PMA/IDS on the ISS.
Then they did the in flight abort, Jan 19, 2020 with the C205 capsule.
Then they flew the Demo-2 flight (crew of 2) with C206 capsule, May 30, 2020.
Finally this is the Crew-1 flight (crew of 4) with the C207 capsule.
So that is history/background. Why is this a big deal? Well this is technically the first operational flight of Crew Dragon. And it will stay at the station for the full duration, with a full crew (well of 4, but there is room for 7, but NASA is only flying with 4).
Is it really a big deal? No. I surmise the news people are desperate for any news that is not politics or disease related. So they are making it a big deal.
The previous one was also crewed (two crew) but it was called "demo" for some reason - despite taking astronauts to the ISS.
The "some reason" that it was called "Demo" is that it was a demonstration flight, not an operational flight.
How is the recent one different?
It is not a demonstration flight, it is an operational flight.
More precisely, it is the first operational crewed flight from American soil with American astronauts in an American spaceship on an American rocket in 9 years, and the first operational crewed flight with a commercial rocket and capsule, ever. It is also the first operational ISS Expedition with an African-American NASA astronaut (there have been multiple African-American astronauts on the ISS during the construction phase as part of Shuttle crews), it is Victor Glover's first flight as an astronaut, it is only the third time that a woman will be Commander of the ISS, and Soichi Noguchi is only the third astronaut ever to orbit the Earth in three different spacecraft.
The reason why you probably think "Why was 'Demo-2' called 'Demo', it didn't look like a demo to me?" is that the demonstration flight went exceptionally smooth. But let's not forget that just one year before Demo-2, a Crew Dragon was destroyed during a static fire test. Also remember what happened on Boeing's Orbital Flight Test (the equivalent to SpaceX's Demo-1), where one bug caused them to be unable to reach the ISS and another bug which they only found during the investigation of the first bug could have resulted in a collision between the reentry capsule and the service module with potential loss of crew and vehicle (if there had been crew on board).
So, these demonstration flights are not just for fun.
The fact that the SpaceX Demo-2 mission looked much more like an operational flight was part coincidence, part confidence. As I mentioned above, one reason is that the flight went very smooth. Another reason is that because of NASA's high confidence in SpaceX, the mission was extended from the originally planned two weeks to two months. Ironically, the reason why it could be extended was the destruction of the test article during the static fire test: this capsule was the capsule that had previously flown on Demo-1 and was intended for the in-flight abort test.
However, because the capsule was destroyed during the fire, the capsule that was planned for Demo-2 was used in the in-flight abort test and the capsule that was planned for the current Crew-1 mission was used for Demo-2. The capsule that was originally planned for Demo-2 was not fully equipped with all necessary systems, so it wouldn't have been able to stay at the station for two months. The original planned mission duration for Demo-2 was two weeks.
So, only because of the destruction of the test article for the in-flight abort was Demo-2 being flown on a capsule that could stay at the ISS for an extended period of time. And the delay caused by the accident investigation allowed the astronauts extra time for training. And because the result of the investigation was that the fault was introduced during refurbishing of the capsule, whereas Demo-2 was flown on a brand-new one (plus, both the process that led to the fault was changed so that the fault cannot occur, and the part that failed was changed for one that cannot fail in the same way), NASA had enough confidence to actually extend the mission from two weeks to 6–8 weeks (it ended up being 9) and have the two astronauts even perform active duty on the station (e.g. Bob Behnken performing two EVAs).
However, none of this was planned, and that's why Demo-2 was a "demo": it was being planned as such, and only ended up being partially operational by accident.
The prior flights where Demo flights, and had test pilots as crew. Crew-1 had "regular" astronauts from NASA and other agencies.
They are all crewed, why is it different? Test pilots vs Passengers.
Think a commercial flight, you won't load up passengers on the first manned tests, you do test pilots and some test crew and such. Then you do the paid passengers. Those astronauts are paying customers of Space-X.
Crew-1 is the first "operational" mission, meaning it's carrying a regular complement of crew specifically to man the ISS. Demo-2, while manned, was a test flight to shake out the Dragon spacecraft - Hurley and Behnken were not part of a regular crew rotation, and their primary mission was to test Dragon's on-orbit capabilities, not to man the station itself (although they did perform a couple of station maintenance tasks while they were there).