Yup. Well, almost. Travelling between countries in the EU is pretty much like travelling between states in the US or provinces in Canada.
You would probably have to show your passport entering and leaving Switzerland though, as they are not a member.
This is the border between the Netherlands and Belgium:
This shopping mall, Rajala, on an artificial island in the Torne river, which marks the border between Sweden and Finland, has Swedish stores in one half of the building and Finnish stores in the other half, which adds a whole new meaning to border trade. Quite convenient also as both countries have a government monopoly on alcohol sales, and here you can stroll between the Swedish Systembolaget and the Finnish Alko to compare prices. Apparently you get a better deal on wines in Sweden but on beer in Finland.
The cities of Haparanda (Sweden) and Tornio (Finland) used to be the same city, straddling the river, until Rusdia annexed Finland in 1809. Now that both Finland and Sweden are in the EU they have merged the public transport companies, so that busses visit both sides of the river, and also passed local bylaws that allow those living in either city to have their kids attend school on whichever side they prefer, so you could be living in a neighbourhood on the Swedish side but have your kids attend school on the Finnish side or vice versa. They wanted to have a joint city council, but as Swedish and Finnish election laws differ too much, that wasn’t possible. So instead they sort it through a number of joint committees.
And after the bridge between Malmö and Copenhagen was built, a lot of Danes have bought houses and condos in southern Sweden. It is only a half hour commute across the bridge, and house prices are crazy in Copenhagen. Likewise, a lot of people from Malmö work in Copenhagen. As it is the Danish capital, there are a lot of well paid jobs there, but living in Sweden is cheaper, so they do the sane commute.
We have a lot of crossborder cooperation with Norway as well, even though they are not part of the EU, they are part of the Schengen area, so there should be no restriction on travel. Since they aren’t within the customs union they may ask if you have something to declare though, but they should not ask for passports.
Typical border crossing between Sweden and Norway: https://youtu.be/m54Qi1fA9YY?si=Ul6NddWjx3nCIbxg
(Most of our border goes through a forested mountain range with very few people living there)
