Baluns are designed to be transformers (like 1:1 4:1, 6:1, etc.) or choke baluns, and both.
For an antenna, the purpose of a choke balun is to create a high-impedance to common mode currents that would flow on the outside of coaxial cable shielding. These common mode currents can cause all kinds of problems such as RF in the shack, matching problems, and others. So, minimizing common mode currents is a good thing.
Common mode currents arise when you are coupling a balanced antenna to an unbalanced line (usually). For example, connecting coax cable to a dipole antenna. You can use either a 1:1 balun or a choke balun at the feed point of the antenna or where the balanced part of the system meets the unbalanced part. The choke balun usually does the same thing as a regular 1:1 current balun but adds the high impedance path to the common mode currents too.
Also, the names Choke Balun and regular current balun are somewhat interchangeable as both are used to do the same thing in ham radio
antenna matching: matching coax to balanced antenna and minimizing common mode currents.
Currently, on my 80-meter dipole, I run 450 ohm ladder line to a 4:1 Current Balun and the remaining 20 feet or so is coax into the shack. In this application, I experimented with both a 4:1 and a 1:1 balun to find the best match and overall SWR on my bands of choice I use with this antenna: 80, 40, 30.
With the same antenna, I have used my own custom made choke balun made from coax turns through 6 toroids -- about 7 turns of coax through all 6 toroids. This worked very effectively except for one thing. This balun was heavy and often would be a factor in my antenna coming down in a wind storm so I replaced it.
So, in answer to your question specifics: (1) they do not always perform the same function but sometimes they do; (2) A regular current balun internally is very much like a transformer where as a choke balun usually focuses on multiple turns through toroids to provide high-impedance to common mode currents; (3) the names are different and some people distinguish between one thing and another by the names and others do not. It is usually not a big deal from my experience unless you are buying something but then you look at the data sheet to understand the balun better.
The image below is of one of my custom made choke baluns. This is an older one that used only five toroids.
The following image shows one of my current baluns, a 1:1 5 KW balun.