Different creatures, different abilities, different rules
While all of these fall under shape-changing, each creature/ability/spell has its own set of rules.
This is a great example of specific over general with regard to the ruleset. Shape-changing is a general rule allowing a creature to change their form, while each instances of Shapechange/Polymorph has specific rules that apply.
When in doubt, do not apply general rules to a specific creature - just use the requirements and limitations stated for that creature.
Creature type vs Ability
Do note that there is a difference in the Creature tag Shapechanger and the ability Shapechanger. Creature tags are important to determine if certain spells/abilities will affect a specific creature (e.g. Polymorph doesn't work on shapechangers). The Shapechanger ability describes something that a creature can do and is dependent on their stat block with regard to how that ability works (as seen above, different creatures change shape differently.)
The Succubus
As you are looking for specific direction on the Succubus (MM, 285) for your campaign, then you need only refer to the specifics of their statblock (emphasis mine):
The fiend can use its action to polymorph into a Small or Medium humanoid, or back into its true form. Without wings, the fiend loses its flying speed. Other than its size and speed, its statistics are the same in each form. Any equipment it is wearing or carrying isn't transformed. It reverts to its true form if it dies.
Given that there is no requirement for a specific Small or Medium humanoid, it can take the form of any Small or Medium humanoid. Tricksy little fiends (note: they are not of the shapechanger creature tag, but are a fiend as stated in their stat block)!
They are different abilities and they work slightly differently
Your interpretation is correct. A changeling PC has no restrictions on the creature type they can change into, only general body shape and size. Doppelgangers can change their size but are restricted to the humanoid creature type (but appendage arrangement is limitless1). Whether you think the humanoid restriction makes sense or not, it is clearly there and there is simply no way to otherwise interpret it. Similarly, the size differences are also clearly written and unambiguous.
It is clear that the Changeling PC's ability has slightly different capabilities than the Doppleganger monster. Note that these two abilities don't even have the same name and appear to have no connection to each other at all beyond beyond superficially similar.
The two abilities were written at different times and published considerably far apart for two different types of creatures (PCs and monsters). But that is not at all unusual, in fact it is more unusual for monsters to have exactly the same ability as a PC. Monsters follow many different rules and have many different abilities, some that are kind-of similar to PCs but not really (multiattack versus Extra Attack for example).
It might be worth noting that the PC version is based on the "change appearance" ability of the alter self spell. Whereas Shapechanger is ability that many monsters have and each version of it is slightly different. Though actually the Death Slaad has the exact same variation as the Doppelganger.
No further clarification has been made that I can find, but I also don't think any clarification is needed. There's simply no reason the abilities would be expected to be the same.
1 - Or limb-itless you might say.
Best Answer
It really depends.
The "basic arrangement of limbs" is talking about being, for example, a bipedal four-limbed bilaterally-symmetric creature. That is to say, you have two arms and two legs, and your right and left halves are more or less laid out the same but mirrored.
A changeling can't turn into, say, a wolf, which has the right number of limbs but in a different arrangement (i.e. four legs, no arms). They also couldn't become a four-armed thri'kreen, because the changeling doesn't have six limbs to start with. I would think this also excludes any sort of "angelic/draconic wings" situation, since wings that are distinct from the arms would represent a whole extra set of limbs, and that doesn't fit into the "same basic arrangement" restriction.
However, if your changeling were, say, a 14th level draconic sorcerer, with the ability to "sprout a pair of dragon wings", then they could indeed imitate any other back-winged creature (but still not a thri'kreen).
However, if the target creature has wings for arms, like a harpy or some sort of bird-folk, that shouldn't be a problem to duplicate. They won't be functional wings, of course, but there should be no issue with turning your arms feathery for the purpose of a disguise.*
As far as tails, it'll probably be up to the DM, but I see no reason to restrict them. It should be fine to give yourself a tail as necessary to impersonate lizardfolk or something. If you want to get really technical, a tail isn't a limb as such, but an extension of the spine -- or to be more accurate, the human spine ends in a tiny vestigial tailbone -- so a changeling would have all the anatomical parts for a tail even though it's completely internal in many humanoids.
*Aarakocra are weird on this front. The art and descriptions up to 3rd edition gave them wing-arms, but as of 5e, the art depicts aarakocra as having both arms and wings as separate limbs, presumably to simplify running them as monsters without wondering whether or how they can draw and throw weapons while flying.