The comparison is that the swordmage and fighter "defend" mechanically in totally different manners and yet are both considered defenders...right?
But a fighter and a swordmage aren't totally different in their mode of defending. Both use marks. An assault swordmage defends by inflicting mark punishment like a fighter (and using teleport rather than lockdown to achieve "stickiness"). The shielding swordmage is the most different, defending via damage ablation. It relies upon other abilities (eg some of the at-wills like Booming Blade and Lightning Lure) to achieve "stickiness".
I wouldn't consider a shielding swordmage a paradigm defender, much as I wouldn't consider an avenger a paradigm striker. I think it's relatively easy to build a shielding swordmage who plays more like a sword-wielding wizard or sorcerer, with a dash of leader. Here's a 7th level version, built using only powers in the FRPG (which introduced swordmages):
* At-will sword burst (AoE force damage), Lightning Lure;
* Encounter 1st level Lightning Clash (two attacks for lightning damage), 3rd level Corrosive Ruin (AoE acid), 7th level Flamewall Strike (wall of fire);
* Daily 1st level Whirling Blade (throw you sword at multiple targets), 5th level Lingering Lightning (lightning bolt vs 3 targets);
* Utility 2nd level Dimensional Warp (encounter power friendly teleport), 6th level Silversteel Veil (encounter self-and-allies defence buff).
That character is not a defender, although the label says otherwise. This is an example of what I have in mind when I say that the role labels are guidelines towards default areas of competence, but not more than that.
If the mechanical way something operates is orthogonal to roles then why are you specifically calling out high AC and hit points as the Defender characteristics?
I didn't say that mechanics are orthogonal. I said that distinct mechanical subsystems for generating outcomes are orthogonal.
For instance, in 4e warlocks and sorcerers tend to achieve mobility via teleporting, whereas rogues and rangers do so via shifting. This creates differences of flavour (magic vs speed and sharp reflexes) and sometimes matters mechanically (eg teleportin can escape immobilisation, can cross water and pits, and can allow gaining elevation without having to climb) but don't make for differences of role. They still produce the same function in play, namely, mobility which (given the action resolution rules and action economy) decreases the likelihood of being targetted, and especially the likelihood of being targeted in melee.
I will note that I find it interesting that on the one hand it's argued that 4e classes have a vastness of flexibility and crossover potential most don't realize yet on the other hand they perform distinct from one another
That's why upthread I've used the phrase "default function". A new 4e player is unlikely just to stumble upon the defending cleric I sketched out above, or the swordmage I've just outlined. And there are some classes that I would never recommend to a beginning player (shielding swordmage, any sort of warlock but especially a Fey warlock, and avenger probably being at the top of that list).
Shouldn't you be looking at the classes as a whole? And if so why can't the wizard's abilities naturally funnel towards defending the party?
A wizard can defend the party. In 4e a cleric or rogue can defend the party. That is not what "defender" means, though.
Defender means being at the centre of the melee scrum. A defender is characterised by being more mechanically effective, and having a greater impact on the outcomes of play, the more enemies s/he is surrounded by. In this way, the 4e defender paradigm has its ancestral roots in the AD&D fighter, who is sticky in melee as a result of the general melee rules for AD&D, but who (unlike non-fighters and fighter-subclasses) doesn't mind being there because of high AC and hit points.
A wizard who relished being at the centre of things - eg via mage armour plus damage-mitigation plus at-will AoEs or ways to use spells for OAs - could serve as a defender.The sorcerer in my 4e game can defend at a pinch, and at late paragon had maximum optimisation for that role (multiple encounter close bursts plus monk multi-class - "drow-jutsu" - to stop enemies getting away, and using his Cloud of Darkness for protection from being hit) but couldn't keep it up for more than a turn or two. Whereas the fighter and paladin can hold that sort of position round after round after round.
The mechanical duration of combats (ie how many rounds, so how much of your limited suit of resources will you need to access to do your thing) is another part of the mechanical environment that underpins the 4e roles. Because 5e combats are mechanically shorter (eg two or three rounds by most accounts) that reduces the scope for the same degree of role differentiation as 4e.
Ultimately (and this IMO is one of the greatest strengths of 5e) neither the fighter or the wizard is, by default, a defender-like character but either can easily step into the role if need be... along with numerous other roles throughout the span of a campaign or even a single adventure... like the controller fighter I talked about earlier or a striker wizard.
Are you saying that either class can be built to be a defender. Or that any given instance of the class - any particular PC - can in one encounter be a defender, and in another encounter be something else? The former claim is about the diversity of builds possible within a class. It strike me as plausible, though I think the narrowness of 4e classes is widely exaggerated. The second claim, which has been made by other posters in this thread, strikes me as implausible. For instance, I don't see how a wizard built using the Basic PDF is ever going to serve as a meaningful defender or healer, nor a fighter build using that document as a meaningful healer.