Polaris type electrical connectors terminology

I have a question regarding Polaris type electrical connectors. I should state right up front I am NOT an electrician, but have done some home wiring and think I know most of the basics.

I am trying to tap into an electrical circuit that is a 8 gauge cable (Type NM-B) (40 amp circuit). I have read about the Polaris type connectors and think this looks like the easiest way to go. The problem I am having is determining what size Polaris connector I need to use. The terminology they use doesn't make sense to me. I am looking at one sight that sells these connectors and (for example) the wire size says "500 MCM – 4 AWG" or another says "1/0 – 14 AWG", those terms don't mean a lot to me so I am not sure what to look for. I can't seem to find any of these type connectors for an 8 gauge cable. I hope that I am making sense, and thanks in advance for any help you can offer.

New Info: So I have read some of the comments below and will try to add some more information on what I am trying to do, I apologize if I am not doing a good job at describing this, I find it hard to put into words what I am trying to do. The 40 amp circuit is for a radial arm saw that is located in my work shop. The 8 gauge cable runs from the circuit breaker box to the shop and ends with a dryer type outlet (sorry I don't know the proper technical term for that). I want to add another outlet of the same type between the existing outlet and the breaker panel for another machine. I want to cut the existing cable and add a box (4" x 4" x 2") at each of those cut ends (2 boxes total). At each of those boxes then "splice" (again that is probably the wrong term – sorry) a new length of the 8 gauge cable to go to the new outlet. Those 2 new cables would then be connected together at the new outlet. I think I would just use wire nuts to make the connections at the boxes, so wouldn't need to go with the Polaris connectors. I have tested making those connections with just some scrap pieces of the 8 gauge and an appropriate sized wire nut and I was able to get a good strong connection that way. I hope this makes more sense. Thanks for your help.