What do you call a keyboard with a bar-shaped Enter key?

Apparently the 'bar' shaped return key is a US layout and the reverse L-shaped return key is a UK/ISO layout - When specifically requesting a reverse L-shaped return key, you can probably ask for an ISO layout keyboard. The bar-shaped enter key is an ANSI layout (according to the comment by the OP).

In my experience the US layout is much more common on laptops (though, I have a British layout Thinkpad), and most English language desktop keyboards outside the UK seem to have bar-style enter keys.

The Gateway keyboard in your image is definitely not the British/UK keyboard layout (as mentioned in the other answer), which doesn't only have different symbol positions but also different key shapes. Its Enter ↵ key is a mirrored ⨼ L shape like the symbol ↵ instead of a 180°-rotated one Ꞁ like on the ISO, UK and German keyboards. It has the Backwards-L layout and the bar-shaped version has the ANSI layout

Backwards L-shaped

A "backwards-L shaped" (or just "L-shaped") Return key is the union of the ISO and ANSI Return keys. The key is often called Big-ass Enter because of its size, or Asian enter because it is found on many East Asian keyboards.

There have been studies that have shown it to be easier to hit accurately than the ISO and ANSI Return keys.

However, with the backwards-L shaped Return key, the \ key has to be relocated, often at the expense of having a smaller backspace or right shift key.

Many many people call it the J-shaped enter key as well. Here is the real US keyboard with that layout

compared to the British one with completely different keys for the symbols

When you see the single-row Enter key, that is the US-ANSI layout. IBM suffered terribly when it added an extra key between Left-Shift and Z on the Selectric III, so when it came to designing the Extended Layout with which most of us are now familiar, someone recognised the folly of the Selectric III and suggested cutting the large enter key in half to accommodate the \ key.

On ISO keyboards, the Enter key is usually still the size of the ANSI Enter plus the \ key and, prior to MS messing up the bottom row with the Windows keys, the \ was often placed in the single space position between Ctrl and Alt. Since the introduction of Windows keys, the placement of \ on ISO keyboards has wandered. Sometimes, the Enter key is narrowed at the bottom so that \ can sit beside “. Sometimes the Backspace key is halved so that \ sits beside =. The last and least desired placement is back in that increasingly annoying position of between Left-Shift and Z.

What's the advantage of a L-shaped "enter" key vs. a regular (one-row high) "enter" key?

IIRC in the past (like 15-20 years ago or more) I've always seen the backwards-L enter key in my country (Vietnam), which uses standard US keyboard layout. On most keyboards the backslash is put on the left of R-Shift key like in the first image, which results in a better typing experience since no keys are too small. On some others it's moved to the left of backspace, resulting in a tiny square backslash key without text label, only a symbol like in the below image. And then when laptops became more common the desktop keyboards began changing to the ANSI rectangular enter key like that.

^{A little bit of my own history: I remembered around 1995-1997 I went to my uncle's house and while playing some spacecraft shooting game I realized that there are 2 similar keys named ← (as you can see in the big-ass keyboard above). I tried pressing the upper one (which turns out to be the backspace) to see if it moves left or not and suddenly I got a much stronger weapon and easily passed level 5, which no one could do before}

While searching on the internet I also find a strange layout where the backslash is moved to the right of the R-Shift key. I don't think anyone will be a fan of this, since typing a backslash is now too hard

FYI Apple did produced keyboards in backwards-L layout like that

Here is a detailed comparison between layouts

A comparison of common mechanical computer keyboard layouts. Keys that are not present in them all are highlighted in pink (alphanumeric) and dark-grey (modifier). Keys that are sometimes omitted are shown with interrupted outlines. Note that the 104th key on the ABNT layout is located in the numpad section and therefore not visible. From left to right, top to bottom:

• 101 keyboard, common in North America, Asia, Oceania
• 101 alternate, common in Asia and Russia
• 102 keyboard, common in Europe, Latin America
• 103 keyboard, used in South Korea
• 104 keyboard, used in Brazil
• 106 keyboard, used in Japan

https://en.wikipedia.org/wiki/Keyboard_layout#Mechanical_layouts

The second version is common in Asia and Russia, which explains why I saw them a lot in the past

You can also see various types of Enter ↵ key if you open Microsoft Keyboard Layout Creator

Further reading

• What happened to upside down L shaped enter keys?
• Why do some keyboards extend the Return key up into the backslash?
• Why oh why are more keyboards ditching the L-shaped Enter key?
• J-Shaped Return Keys
• any chance to order a keyboard with this (customized) layout?