Well, if you want it that way in your lil' cornor of the Trek 'Verse, sure. I'd argue against it, tho. 'Course, there are plenty of real-life examples wherein ships look very, very close to the same - such as a lot of the US Navy's SuperCarriers - but are of different classes. So, there's one argument for. However, in my Trek 'Verse, if they look the same externally with maybe some minor exceptions, then they're of the same base class. Allowances might be made for sub-classes, but for the most part they'd all be of the same class. YMMV, as always.
I suppose it depends. There are certainly some classes like that in fanon, because they are effectively subclasses and look little different from the original class. For example, Ships of the Star Fleet includes classes like the Achernar and Bonhomme Richard, which are subclasses of the Constitution family and thus are very similar in appearance and capabilities. Naturally it would be wise to limit the number of such classes, since otherwise people would get confused.
A class is defined as something which is (1) visually recognizable as being of the class in question and (2) having performance and capability ratings within a certain design-specification range. The upshot of ship "classes" is that you can determine, what ship type to use in a specific function based upon the class, and not have to know the minutiae of a thousand unique ship designs. So... in answer to the original poster... absolutely you can have two ships that look identical, externally, and yet are of totally different classes. Let me give you a hypothetical example. We all know that th Galaxy Class was designed as a long-range "mobile city in space" concept, intended to operate well beyond the borders of known space for extended periods of time. Agreed? Now, suppose that a partially-completed Galaxy were outfitted significantly differently... in the following manner. The secondary hull would remain almost unchanged from what exists in a Galaxy class. However, the primary hull interior volume might be dramatically different, with half or more of the volume taken up by embarked-craft storage. The mission role of the ship would be dramatically different. It would no longer be suitable for the missions which the Galaxy would serve. It would, however, be suitable for missions for which the Galaxy would NOT be suited. And yet it would look identical, or nearly so, externally. This class would be a "supercarrier" rather than an "explorer" and would, as is always the case, be named after the first ship built in that general configuration. It would not be referred to as a "Galaxy Class" because that would simply cause confusion... and as such would be counterproductive. The Chief of Starfleet Operations needs to be able to move and reallocate assets without knowing every tiny bit of trivia about every ship. He'd just know that you send the Galaxies to do this job, or that job, and you'd send this variant Supercarrier type vessel to do other types of jobs. That's why groupings of "ship classes" are used. And, as I hope you can see, it's an important function. It makes it possible, even practical, for a human being to know what the heck is going on!
Well, there's a rumor that Daniels was in the 601 Club visiting the 22nd century, had a 24th-century Akira-class schematic displayed on his PADD and dropped it on the floor, and the guy who picked it up and handed it back was the future designer of the NX class.
A good modern example of this is the Spruance and Kidd classes....they are basically the same visually, but the Kidd's have a superior AA capability and were originally commisioned for this role by Iran!! http://en.wikipedia.org/wiki/Kidd-class http://en.wikipedia.org/wiki/Spruance_class_destroyer
...Which sort of relates to the prime reason why two identical ships may belong to two different classes: their class names were given by their two different operators. Spruance, Kidd and Ticonderoga can be distinguished from each other simply by looking at the silhouettes. The American, British, Canadian and Australian versions of a common destroyer or cruiser class in WWII often could not, either because the exteriors were identical, or because every last nut and bolt was. And pre-owned warships further stir the cauldron: ex-USN Garcia or Perry frigates currently serve under a dozen different class names across the globe. Starfleet probably is too much of a unified body to assign multiple class names to identical ships for mere organizational subdivision reasons. That's not completely impossible or unheard of, though: the medical ship in "All Good Things..." says Hope class on the dedication plaque, while the Encyclopedia suggests that an identically shaped (unseen) vessel in "Interface" was of Olympic class instead. I could easily see Starfleet pulling aside a few Olympics, giving them medical innards, and renaming the variant Hope class. Then again, even unified bodies can give multiple class designations to what is basically a single design. The Royal Navy mass-produced destroyers before WWII in batches of 8+1. Each batch was named after a letter of the alphabet, so e.g. the A class had eight identical ships with names beginning with A, plus a ninth, larger vessel for flotilla command that was still considered part of A class but didn't follow the alliterative naming scheme. The B class was completely identical to A class, but nevertheless considered separate. C class went to Canada wholesale and was locally considered part of the River class, combining select ex-RN destroyers from multiple "letter classes" and renaming them after local rivers without any alliterative ambitions. D class introduced various improvements, while E and F were further modified but identical to each other. And so forth until I class... During the war, the RN also built a new C class when it ran out of letters, and divided it into four subclasses of eight: Ca, Ch, Co and Cr, with alliterative names on those first two letters. If you can still follow, be relieved that Trek fandom has only come up with a fairly simplistic class/subclass/variant name scheme so far... I could see the Miranda family as a close analogy to those British destroyers. Initially, there'd be just a couple of batches, like the ones suggested by Todd Guenther in Ships of the Star Fleet; each batch would have its own class name, whilst there'd be some design variation between and within the batches. Further batches would be built in the late 23rd and early 24th centuries, some possibly still given separate (sub)class designations - but at some point, Starfleet would stop caring, and would simply retroactively name all the slightly different ships Miranda class collectively, perhaps after the name of the first or latest ship/batch in the general family. Timo Saloniemi
The Saladin class destroyer and the Hermes class scout look virtually identical, but have utterly different missions. For a real life example, take a WWI era destroyer which has be re-outfitted as a minesweeper. It looks the same as other vessels which have not been converted, yet it is a different class.
Why not? After all, the Sovereign-Class, Oberth-Class & Excelsior-Classes have all been externally identical and internally been rearranged & recertified for specific missions all over the place. Frankly, it doesn't really matter, a good ship & crew make for a good story regardless of the treknology arrangement. Just my $0.02 Regards, Jason K.S. Hauck, "Star Trek: Hell's-Gate"