As mikes answered, these connectors are a type of Molex connector. (Or they may be their generic equivalents, if any.) Molex is a company/brand. It has several types of 2-pin connectors. The connectors in my OP pictures are part of either Molex’s “Mini-Fit Jr.” trademark of power connectors or a generic equivalent (if any; I don’t know whether generics are permitted to be made).
Molex’s Mini-Fit Jr. diagrams considers the plastic connector that gets partially enclosed in its counterpart connector when mated as the receptacle, perhaps because the receptacle permanently houses the socket (female) terminals. Molex considers the plastic connector that partially encloses its counterpart connector when mated as the plug, perhaps because the plug permanently houses the pin (male) terminals.
I don’t know what the connectors in my OP question are called if unbranded, so I’d also appreciate an answer that can give unbranded but specific names or search-friendlier branded names. This question discusses the difficulty in web-searching for Molex and generic or other-brand connectors, the shortcomings of related nomenclature, and the usefulness if the nomenclature were to have some basis in chamfered keying permutation, and it lists a few brands. In web searches, the Molex items can almost only be disambiguated by their manufacturer model numbers. Without first knowing the number or uniquely identifying unbranded terms, some trial-and-error options are image searches or searches on manufacturer or retailer sites with specific categories. Waytek has the category:
Terminals & Connectors > Multi-Pin Connectors > Mini Fit JR Connectors.
It’s difficult to find these connectors on Molex’s website even with the model numbers, because it gives overly-generalized reference pictures, sometimes with a different number of circuits (i.e. corresponding pins or wires), of the model’s containing series. Waytek gives more specific pictures. (I’m not affiliated with any party, but this is how I best found the info in the absence of clearer nomenclature.) There are several models of Mini-Fit Jr. connectors. Going by Waytek’s nomenclature, the items in my OP question appear to be the following or their generics (if any):
The plug is Molex 39-01-2021 Mini-Fit Jr. Connector, 2-Pin Panel Mount Plug.
The receptacle is Molex 39-01-2020 Mini-Fit Jr. Connector, 2-Pin Receptacle.
The pin terminal is Molex 39-00-0041 Mini-Fit Jr. Pin Terminal, 24-18 AWG.
The socket terminal is Molex 39-00-0039 Mini-Fit Jr. Socket Terminal, 24-18 AWG.
Their corresponding extraction tool is Molex 11-03-0044 Mini-Fit Jr. Extraction Tool.
The only crimp tool I found named by Waytek specifically for Mini-Fit Jr. is Molex 63819-0900 Mini-Fit Jr. Crimp Tool, which is expensive. Molex’s corresponding Application Tooling Specification Sheet lists the aforementioned terminals’ model numbers as compatible.
A cheaper crimper, named by Waytek but not specifically for Mini-Fit Jr., called the Molex 63811-1000 MLX Hand Crimping Tool, 24-14 AWG, applies to the desired gauges, but the corresponding Molex Application Tooling Specification Sheet doesn’t specify the aforementioned terminals. But the “Application Tooling” section on the righthand side of Molex’s product page lists some models of terminals that seem to have pins shaped similarly to the desired one. Also, the corresponding Amazon listing includes the phrase “For Mini-Fit Jr.” in its title.
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