People say exploration and isolation a lot and i don't think those ideas are truly expanded enough, or clearly defined. You can find almost any game with exploration; RPGS, open world sandboxes, etc. When you say exploration I feel like maybe you mean completion (that's how I think of it, as you'll read later on). Like getting items and powerups as a reward for checking the nooks and crannies. Isolation I find is more a matter of opinion, as I consider Samus not isolated due to being surrounded with enemies of different race and levels of sentience constantly. whereas you may consider her isolated because she is without allies in a hostile land.

What I think makes a metroid game a metroid game in terms of visuals and audio, is it's style, and it's story telling. The music is almost always atmospheric, the lands/areas almost always dark, or mysterious at the least, with varying degrees of danger. Bleak, overwhelming at times, with Samus being the only sense of hope in the land.
The story is told most importantly not by what is said to us, or Samus, but by what we experience. What we see and do tells the story without words and is I think, combined with the music and the style, the most important aspects of a metroid game without considering gameplay.

In terms of gameplay it's the puzzles combined with the natural obstruction of your path that, what I think, makes a true metroid style game (if it's going to be a full fledged metroid game you'll need all that jazz I was talking about above).
Your goal is to get from the start to the finish, and to do that you have to surmount obstacles every which way you try to go. There is usually only one path to take, but you don't know which it is. You blindly batter your way through hoping your efforts aren't in vain, or hoping that you didn't miss something crucial. You're required to remember your surroundings and think about how you might be able to apply your new abilities to advance the game. Upon forgetting or not being creative you are now forced to go back and study your explored areas till you find a new path.
This is the biggest thing with Metroid. Being stopped, obstructed, redirected, you name it, but in a way that doesn't just look like the developer put a brick wall up in your way that reads "YOU MUST HAVE THIS ITEM TO PASS" or "YOU MUST HAVE KILLED THIS BOSS TO PASS". You have to be creative to work around it. It's a puzzle(albeit beams and missle doors aren't very creative, nor metal doors a la super metroid).
As far as "exploration = collection" I said before is concerned I think it's a strong factor to the "overcome the obstacles and puzzles" challenge, because there are plenty of enemies that are obstacles, as well as bosses, and every powerup helps combat that particular set of obstacles. Though diminished in rarity and power missle tanks, energy tanks, and so on, are a very key player in progression, and you'll need more or less depending on skill.

I don't know if I've fully, and correctly illustrated what I think, but I hope I have. It took me a lot of thinking, and I recently beat Super Metroid Hyper, Super Metroid Redesign: Axiel edition, both of which are super metroid hacks, and I just beat Axiom Verge aswell. Though the first two share name and style with Super Metroid, it doesn't mean they would share design aswell, and though Super Metroid Hyper did have a few too many brick walls for my liking (metal doors!!), I found they were great examples of core design when concerned with Metroid gameplay.
Axiom Verge aswell, though only just learning about it, I fell in love immediately and felt like I was playing another metroid game. I could go on about what things I think took away from the metroid feel but that's not the topic, and speaking of exploration that's definitely a game that requires exploration for explorations sake. I consider Axiom Verge another great example of core game play design that falls in line with what it means to be a metroid game.

That's my 2 cents, thank you for reading.