What are the advantages and disadvantages of either bulb shape here? they are both 400W MH but they're different in design, why?

Honestly, I like the BT28 design because it can be supported by an insulated support on the top/front of the lamp, so on a BT37 lamp, the weight can be supported if it's mounted horizontally.  With the ED design, this would be difficult/impossible to do, however on the ED design, the arc tube has better support against vibration

Is there a list or table anywhere that lists the different bulb shapes by number..?

Ria in Aberdeen

that'd actually be quite nice.

A list would be nice. The letter usually designates the shape and the number, the diameter of the largest part in eights of an inch. Here's what I can think of at the moment :

T : tube (such as a standard fluorescent lamp or any tubular shaped lamp)
BT : blown tubular (a "blown out" part of a standard tube. The "knob" at the end of a HID lamp is part of the "not blown" tube.
E : Elliptical (mainly HID)
ED : Elliptical with a dimple for support wires (mainly HID)
A : standard shape of GLS incandescent
R : reflector
BR : bulged reflector
G : globe
C : candle (usually Christmas lights but not always)
S : straight side
F : flame
There are others. Some manufacturer web sites have lists and some have drawings as well. There are many others.

As far as why manufacturers have some HID in BT shape and others in ED shape, I believe this is to facilitate the tooling requirements at the factory. The consumer is "not supposed to care" because either lamp type "will give stated lumens". M250R201SA has a point, though. However, I believe the lamp manufacturers don't really care about this.

Early coated BT mercury lamps were done so because the "unblown" part of the tube at the end could be left clear so the supporting frame would not scratch the phosphor. In these lamps, if pieces of phosphor fell onto hot parts (such as the arc tube) it would lead to premature failure. That is why some old lamps are clear at the end. Later, chemical composition of different materials were improved to the point of this becoming a non-issue. Manufacturers started making fully coated lamps in BT (because they already had the tooling) and in ED (a newer style, maybe more familiar to the consumer so more "desirable").

As far as BT clear mercury lamps, they were done so because the factory already had the tooling for that shape. All they needed to do was stop the phosphor coating step and change the etching stamp.

Is different lamp shapes under some patents like for example the bend style of pl-lamps?

Maybe some time ago, but those would have run out by now. PL lamps are not exactly a booming industry, so manufacturers probably will keep the existing factory tooling, which explains the different bend shapes they have. I believe the different designs are now kept by tradition instead of any other reason.

Sorry As Being New To All of This Which Of Those Lamps Go With Which Letter?
As in The Top Lamp is Letter???
And
The Bottom Lamp is Letter???
Thanks All

***Also Please Note that I'm on Heavy Meds right Now So if My posts sound Slilty off You know why***

Assuming you're talking about the picture in the original post, the top lamp is BT and the bottom, ED.

The top lamp would be BT-37 which is 4 and 5/8 inches diameter and the bottom lamp is ED-37 which is also 4 and 5/8 inches diameter.

Assuming you're talking about the picture in the original post, the top lamp is BT and the bottom, ED.

The top lamp would be BT-37 which is 4 and 5/8 inches diameter and the bottom lamp is ED-37 which is also 4 and 5/8 inches diameter.

I Was, Thank You as You can see replying or asking questions on Heavy Med sometimes makes for strange posts.....