There is a chance that a couple of terms are getting mixed up here.
There are millions of people traveling worldwide every year and there are many many different rules in different countries who wish to control people crossing their borders, and often different rules for different nationalities crossing the same border, and different rules for people of the same nationality but in different circumstances,
At its root, a "Visa" is a permission given to an individual by a country to cross a border into that country. Sometimes it is a stamp in a passport, sometimes it is a piece of paper attached to a passport, sometimes it is a piece of paper not attached to a passport with or without a stamp in the passport. It always comes with conditions and rules.
A tourist visa, for example, can be to enter Turkey. $20 US and you are in (I think it is 20). No application needed for many western country citizens, just pay your money and enjoy your vacation.
Or, it could be what is required to enter Russia. Lots of paperwork, lots of money, lots of restrictions.
Or if you are a US Citizen, going to Canada or Mexico, you get verbal permission from the dude or dudette at the border or airport upon presentation of either your passport or the little plastic card issued with your passport. No fuss, no muss, just long lines. I remember when all you had to do was show your driving license, no passport to go in and out of Canada from the US.
Europe is a different kettle of fish. Many of the European countries, but by no means all, have banded together to sign the Schengen Treaty which allows free movement across member states borders, with no more hassle than driving from Alabama into Georgia, or Colorado into New Mexico.
There is a border around all these member states, and anybody requiring entry from any non-Schengen country needs permission. The required permission can be in one of at least 3 different basic ways.
For citizens of the non-Schengen European Union or EEA such as the UK or Norway, we need to have our passports checked when we enter the Schengen area and then have EU and EEA right to remain and work.
For citizens of certain countries such as the US and Canada it depends if the intention is to work or remain a long time or not. For stays within the Schengen area of not more than 90 days in any 180 days (cumulative for all Schengen countries visited or transited) where no work or settlement is undertaken or contemplated, those citizens may enter under a strictly enforced Schengen Visa waiver program where all that is required are the usual entry and exit immigration stamps. That's not stamps for going between Schengen member states but in and out of the Schengen area.
If a citizen of the US or Canada wishes to enter the Schengen area to work, to settle, to stay longer than 90 in 180, or various other conditions they need to get a specific visa - which varies by circumstance - from either the first country they will enter or where they will spend the majority of their time, and the Schengen visa waiver program will not apply.
For citizens of other countries they either qualify under the Schengen visa waiver program, or need a Schengen visa from their port of entry, or need a different visa, depending on their citizenship, origination point or other criteria.
I hope that clarifies it - a little.
I neither work for the Home Office, the Foreign and Commonwealth Office, nor am I a lawyer; nor do I play any of the above on TV.