It may or may not be correct according to the vendor, but I've seen plenty of these with the wire soldered in to the small part.
If your wire isn't spreading out to create a good electrical and mechanical contact as previously mentioned, then soldering it to the smaller threaded insert would be the way to go.
Personally I prefer the retractable + stackable types, such as
Mueller BU-3261410. And there are decent copies of these that won't break the bank (genuine Mueller's are a bit over $5 a pop; copies can be had for ~$1 per and are decent -
example).
Other quality brands to consider would be Pomona or Cal-Test next time you're in the market.
And there are also decent silicone insulated patch cords IME, using both retractable & non-retractable connectors in various colors (beyond black & red). You can even get silicone wire on eBay in small lengths in various colors as well (I currently have some 20, 18, and 14AWG on hand).