Does the addition of chlorine to carbon-carbon double bonds proceed through a halonium ion?

I need some serious help with the mechanism of ionic addition, both my textbook and my teacher are at odds with internet videos (khan academy) which both seem to be at odds with quote, "recent evidence" on the topic.


I don't need to know much of this for my exam, but basically I want to understand it properly because I hate the idea that my foundation is built up badly from the start.


Here's the deal:


During the ionic addition of say, Bromine-Bromine to ethene, my textbook says that 'recent evidence shows' that there is a 'bridged structure' formed when the diatomic bromine breaks up and attacks the double bond.


I get this, the bromine becomes polarised when approaching the ethene at a right angle, leading to one bromine atom losing an electron to the other, more negative bromine. 


This positively charged bromine which is two electrons short of a full shell now needs two bonds, right? So it attacks the ethene double bond, forming the 'bridged structure' my book mentions by bonding with each Carbon on the ethene molecule. Fine. Cool. Then eventually the other negatively charged bromine atom can form a bond on the opposite side of the molecule from the first bromine, leading to a lovely looking (1,2)-dibromoethane:


[![This seems logical, right?](https://i.stack.imgur.com/PcyMk.png)](https://i.stack.imgur.com/PcyMk.png)


Except now, my book goes on to completely ignore what it just did during the exact same process with Chlorine gas, which makes no sense. No bridged structure, the pictures even say that the Chlorines end up on the same side of the molecule as seen on wikipedia and on any quick google image search of 'addition reaction':


[![This is what you get when googling 'addition reaction', but surely this is wrong because the chlorines must be on opposite sides of the molecule?](https://i.stack.imgur.com/sap4X.png)](https://i.stack.imgur.com/sap4X.png)


I've seen this in different places on the web too... Bromine somehow undergoes a different ionic addition than Chlorine which makes no sense, it basically bonds to one carbon even though it needs two (like the bromine did), so no bridged structure.


I don't get it folks. Bromine and Chlorine have the same valency, and they're more electronegative than Carbon or Hydrogen. Why are these two processes different, and why do they end up with significantly different products?


