Well the methods are similar. in some, you twist the wire and then solder it. As I have worked on electrical components that need minimal heat, I tin the ends such as this site shows.
http://www.teamnovak.com/tech_info/how_to/solder/index.html
That link looks like the tinned wires are just butted together and then soldered. Wouldn't that make for a weak connection where the wires are held together where the solder is the only connection between the 2 wires?
I usually solder the way shown in the 1st link and have never had a problem with it.
Is it pronounced "solder" or "sodder"?
Yes, you are right. If you can help it, try not to simply solder two tinned leads side-by-side. Interleave or twist in some manner to increase the surface area that the solder has to hold on to. In either case the solder is still the only thing holding it together, but the tinned side-by-side solder is much more prone to mechanical failure.
Now as Eldar said, if you are in a heat sensitive circumstance it might be beneficial to tin the leads before soldering, but this is usually the case when soldering a wire to something else that might already be tinned.
In general, if soldering two wires together, interleave then solder. You may feel like you need an extra set of hands when doing this but what I do when soldering wires (which I do for a living), and I need an extra hand I use heavier solder and I either hold the smaller spools in my mouth or put the heavier spools on the bench and bend the solder to where I'm working. That way I can hold the wire in one hand and the iron in the other.
That said, honestly, if the wires are properly secured and you avoid like the plague soldering wires together at stress points like in the neck area where side to side movement is going to happen, either case is likely going to be trouble free. The number one problem I see with soldering is cold joints. The Solder should flow extremely well into the joint. You don't need to move the iron around, just hold it in one spot until the wire sucks up the solder like a sponge. You're not just trying to pile solder on top.