they basically mean the same thing, at least virtually all the time.
different programming languages use different terminology. I'm a bit rusty with VBA terminology, but the two in question would be Subroutines and Functions.
here's a subroutine (that does nothing useful):
Sub AddTwoNumbers(Number1 As Integer, Number2 As Integer)
Dim Result As Integer
Result = Number1 + Number2
i think, technically, you got it spot on, but in reality, they are used interchangeably. Number1 and Number2 are the parameters for the above subroutine. If you see "argument", just keep in mind that it's just "stuff" (integers, strings, the list can get really long) passed to a sub or function.
Don't worry too much about that "method signature" stuff you may have encountered in your google search. It will never come up in VBA, though being a professor, if you're curious, a method signature refers only to the return type and parameter types of a function/sub. For example:
Function Example(Words As String, SomeObject As WorksheetFunction, SomeRange As Range, SomeNumber As Long) As Boolean
Example = True
the method signature of the above function would be:
String, WorksheetFunction, Range, Long as Boolean
method signatures have to do with concepts foreign to VBA such as overloading, delegates, anonymous types, and no, i'm not explaining those, lol.
i've learned a lot from people who have freely shared their knowledge online, in appreciation, i try to give back. So if you have other questions, post to this forum, it should be a while before you continuously stump me for answers.
good luck on your journey into the world of programming. :)
p.s. This response was written in camelCase, another term you may encounter if you end up outside the world of VBA. ;)