So the Orange Wonder is demanding the that fleeing residents from the Bahamas have proper documentation before they are allowed in the US - CNN is reporting. I really doubt they have anything left much less proper documentation. Now if they were white and wearing MAGA hats I'm sure they would be let right in.
It's worse than that. They aren't even letting them evacuate temporarily
with a fucking passpost! Now they are having to apply for an actual visa in addition to having the passport. It's pure racist bullshit, and the INS and DOJ are going right along with it.
for a "world traveler", you are surprisingly confused. The stamp you get on your passport when you visit a foreign country IS your Visa. So "showing your passport" and "applying for a visa" is the same exact thing... unless you are claiming to be visiting for work-related purposes, or to stay permanently.. then that is of course a different story.
Unlike you, I have been to places that actually require visas and have a decent amount of first-hand experience with them.
To get a visa you submit an application to the embassy or consulate of the country you wish to enter. There will be a form, likely a picture must be included, there is always a fee. In some cases there is also an interview requirement--AFIAK always for the US but rarely elsewhere. That gets approved or denied, if approved you get a stamp or a sticker in your passport. When you arrive you will likely get an entry stamp. Note that if a visa is required and you don't have one you aren't even going to be allowed on the airplane. (And, yes, they most certainly do check. Twice I've had them tell me I didn't have a valid visa when they didn't look carefully enough.)
There are also a decent number of countries which use a visa-on-arrival system. You can do the application when you land at the airport.
When you're a first-worlder going to a first world country you generally do not need a visa. You simply show up and they stamp your passport when you get there.
Here is a comparison of what US and Bahamas passports permit:
https://www.passportindex.org/comparebyPassport.php?p1=us&p2=bs&fl=&s=yes
I find this very strange as it shows Bahamas do not need a visa for the US, although everyone who doesn't needs an ESTA. (Basically a visa-lite. Purely electronic, you fill out a form, pay a much smaller fee than a usual visa and assuming there are no red flags on it you get permission to enter.) Perhaps the hurricane has something to do with this--plenty of those fleeing the devastation have neither homes nor jobs abroad and thus will look like prime candidates for overstaying.
I don't think this is racism, though--US border policy has always worked on a basis of presumed guilt. It's your job to show them that you're going to go home rather than overstay.