Lets imagine that you know how to program Microsoft C# (for example). There's a good chance that if you joined a company who use Java or VB.Net, you could easily, with a bit of time and effort, program either of these languages with no problems. This is because pretty much all languages essentially use the same methods to control what happens in a given routine.
Almost all languages have If - ElseIf - End If statements to control the flow of logic, it's just a case of understanding how to write this statement in your chosen language. For example:
VB.Net
If x = y Then
Do Something
Else
Do Something Else
End If
C#
if( x == y ){
Do Something
}else{
Do Something Else
}
Both of the above do exactly the same thing but the VB.Net way of writing is slightly different to C#. The common ground is Programming whereas the differences are Syntax.
That is an answer to your question at the most basic level. I can hear people saying "the statement 'The common ground is Programming whereas the differences are Syntax' is not correct, He's missed the point" and this is true to a certain extent (I'm trying to keep it simple).
Programming is all about finding ways to do things. There are always 10 different ways to solve any one problem when writing an application. Which way you choose (and the reasons you choose that way) is the real essence of programming. One way will be really quick, one way will really efficient in terms of reusability. One might adhere to Object Oriented prinicples whereas another might not need to.
As I'm sure you've seen, there are hundereds of books entitled 'Learn XYZ in 24 hours'. I used these myself years ago and basically they're not really worth using IMO. As somebody once said, "You can't learn to program in 24 hours but you can learn to program badly"
For this reason I'd agree with you original source and say learn to program and then worry about what language you want to use. The chances are that if you get a job in the future you'll have to be pretty flexible anyway. Ultimately you do need to use a language in order to learn programming as you can only take examples from books so far before wanting to try stuff out for yourself.
Try looking into Design Patterns and Object Oriented Programming
Hope this helps.