Sorry, no. CoD and HL2 are only superficially similar, and are on separate branches of the fps family tree.
All the points you raise are reasons that HL2 is better, but not categorically different. HL2 has more interesting weapons, level-design and enemies, but it's still a scripted, linear corridor shooter built around nominally interactive set-pieces. Structurally it's very similar. For example, framing the levels as a continuous journey instead of discrete scenes was a good design move, but modern CoD's don't make you restart levels anyway so it's just a matter of elegance of presentation.
They are similar in that they are both linear shooters with scripting.
Structurally they are very different. A typical CoD game has multiple player characters, in multiple locations or even time periods. Levels are discrete locales, with cinematic briefing intros and outros. When you finish one level, you either go someplace else entirely to get up to date with what's happening with another player character, or you get a message like "90 minutes later" and continue with the same character as he continues his adventure in a new place. There are some exceptions to this -- occasionally a subsequent level really is just a continuation of the previous area -- but even then you get between level briefings and situation updates that mark out each level as a discrete entity. In Half-Life, you start the game, and you play the game continuously, going from one connected area to another, until the game is done. Level transition is marked by a brief "Loading" text, but one level flows seamlessly into the next. Every hour or so, you'll load a level and get a brief text display of the chapter title. Chapters mark thematic or narrative progression only -- the game world and the player experience is still one continuous experience. And of course you have just one player character, experiencing the whole story, from beginning to end, in one linear -- no jumping around in time or place -- stretch.
In terms of linear level design, Half-Life and CoD are both linear. What distinguishes Half-Life's linearity from Call of Duty's linearity, is that in Call of Duty there is never a question of how you will navigate your environment: it's nearly always a design corridor. In Half-Life, there's only ever one way that you're going to navigate the environment, BUT the path through the environment is often quite complex, and much of the gameplay is FINDING THE PATH. Think the laser trip mine warehouse in Half-Life 1: there's only one path, but the gameplay of the level is about finding that path without blowing yourself up; the headcrabs are there not as combat threats to you, but as dumb automatons that might set off the mines. Finding a path forward is NEVER a gameplay element in CoD. That is a huge difference, particularly when you consider that even Doom had clear navigational check points -- locked doors with color coded keys -- that in most cases had to be navigated in sequential order, i.e. truly non-linear levels are a rarity in shooter design. In other words, it's not linearity per se which separates shooter level design but whether you make navigating a path through a level part of the gameplay -- even if there is only one path -- or not.
Finally, if we're gong to say that there is no categorical difference between these gameplay elements, then there really isn't any categorical difference between shooters at all. Given that certain shooters have similar characteristics that are dissimilar from other shooters, I think it is perfectly reasonable to distinguish between different kinds of shooters. A Call of Duty clone plays nothing like Half-Life. If you've played both games, and are still saying that they play very much alike, then you aren't paying attention, or have such a small basis of comparison that you can't distinguish between pretty big differences. To a 85 year old grandma, Mario Kart and Halo are both just video games; if you actually play video games, they're pretty darn different from one another, and if you play shooters in any volume it should be completely obvious that Half-Life and Call of Duty are worlds apart from one another and represent entirely different schools of first person shooter design. But hey, they're shooters, they have scripted elements in their levels, and they're mostly or entirely linear, so therefore they're just like each other, just like Mario Kart and Halo.
And of course much more examples.
