I'm not sure if anyone is still looking at this thread line, as it seems to be a few years old (Ok, 9 yrs, but still) but I found it in my search about Tank vs A-shirt so in case others do as well, here's a longer AE response from someone else in the US:
Muscle Shirt - A type of men's shirt, basically like a crew neck T-shirt with the arms missing. Fits all the way around the body, arms, and neck. I think these are typically in a cotton jersey. Similar shirts in women's apparel are basically just tank tops with wider straps. May be white or in color, may or may not have a printed graphic or saying.
Tank or Tank-Top - (note - probably so named as it is the kind of shirt often pictured worn by military in tanks, perhaps because of the heat of being in an enclosed space.) A shirt without sleeves, with 1-2" (or so) straps, often a scoop neck or V neck (not usually the close crew neck fit of a muscle shirt), possibly larger arm holes than a muscle shirt. Refers to any shirt with this kind of shape, whether a thin white jersey or rib knit typically used as an undershirt, or a thicker rib or jersey shirt in an array of colors meant to be worn as a stand alone shirt or in layers, or a patterned or embellished shirt of most any material, on up to a fully sequined top as part of a women's dressy outfit.
A-Shirt - From what I can tell, a men's Tank Top (though strictly in jersey or rib knit or something appropriate to the term "athletic"). I don't know about the distinction of designed to be worn alone vs under another shirt - we're awfully fond of layering as it is so many shirts that can be worn alone may often be in layers, and sometimes shirts meant to be undergarments are worn alone.
Wife beater - not in common use as in prior years in the US for social/politically correct reasons, but I always pictured this to be more of the specific style of white rib knit tank top that has a very narrow back, as if very wide arm opening, but other online sources indicate muscle shirts could also be referred to as this.
Vest - I guess from the above conversation usually referred to in BE as a waistcoat? A "vest" can be any sleeveless garment typically worn over a sleeved shirt, but takes a few forms in the US: Typical vest is the middle part of a 3 piece suit or tuxedo that covers the shirt and goes under the jacket, usually made of wool or silk (but could be made in any suiting material.) A sweater vest is a knit garment designed to wear over a button down shirt for men, or a blouse for women, often with cable knitting or some other distinctive color or textural pattern. A knit tank top could potentially be used as a vest if worn over another shirt, or could be worn alone. I would tend to think of a knit tank top as a thinner item than a sweater vest. Sleeveless outerwear garments such as zip-up polyester fleece are also called vests. Lastly, strap-on Kevlar protective garments for law enforcement officials are called bullet-proof vests, which can be worn under a sweater or coat or as the outermost item, but usually still over another shirt of some kind.
Camisole - Women's under shirt typically with spaghetti straps, usually a thinner silky material akin to a top-only slip. Occasionally a tank top of similar material &/or with lace embellishment may be also referred to as a camisole.
Shell - A dressier women's shirt designed to be worn under another top or jacket, allowing a V or scoop of the shell to show through at the neck. A dressier alternative to a typical tank top (shells are usually a polyester or silk, often with lace or bold colors, thicker than a camisole, often created reversible in a different color.) Sometimes a solid color tank top in a dressier material may be referred to as a shell.
Until reading this thread I had never heard of the term "singlet".
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