Why do you call it a "life deck"?
In 1999 CCG's were all the rage. Magic and Pokemon were the biggest two at the time but we were in an odd age for either. Pokemon was for little kids. Magic was too dark for most of our parents to let us play. We didn't have our own money to spend. If we were 4 years older or younger we would have gone with either of the two.
So what did that leave us with? Most friends were playing the Star Wars CCG by Decipher but the game itself was complicated. Most of the other options out there were general scifi/fantasy themed card games like Xena, Star Trek, Lord of the Rings, and such. Nearly every niche fandom had its own failed CCG by 2001. I did have (still have) a ton of the X-Files CCG which works more like Clue and not conductive to play against people who didn't have every episode memorized and could figure out the opponents X-File card after a few turns.
Enter the DragonBallZ Collectible Card Game. This came out in 2000 and was made by Score (now Panini). This game was the first CCG I played where the cards made sense and I knew who all the characters were. We used to rush home after school to make sure we caught DBZ at 4pm or else we would miss what was going on in the story.
When the game came out the initial set covered only the Saiyan Saga. You had starter decks which, in this game, were required to start playing as they contained 3 main personality cards that were not available in boosters. Think of these as commander cards that are always out and don't need to be cast from your hand.
Your main character card started out at lvl 1 and had more levels they could achieve during the game which made them stronger and gave them more abilities. This is more like Pokemon evolution with basic, stage 1, stage 2, ex whatever. They were also kept outside your deck and had a separate mechanic to level up. But on those personality cards is a list of numbers representing available stamina for attacks.
The rest of your cards were normal game cards that made up your life deck. (Finally I get to the point!) There are no mana or energy cards in this game so you pay for a cards ability using either the stamina numbers on the personality card or by discarding cards from your life deck itself. Physical attacks typically did physical damage (stamina) and would make the other player lose the ability to pay for stronger cards. Energy attacks were the ones that typically did damage in the form of card draw at the cost of some amount of stamina.
You could win the game by either leveling up to your highest personality card level (Which was lame so we didn't do that.), playing all 7 Dragonball cards in your deck, or bringing the other players life deck down to zero. That's the version we played.
So we played this game for like four years, and ever since then a players deck has been the "life deck" to me.
I only bring this up because Mark Rosewater recently did a podcast episode on the history of the design on the back of the Magic the Gathering card. How they were stuck with the word Deckmaster on the back even though its not a thing and they can't update the logo etc. But in that episode he went over why it's called a library. Because the cards are "spells" and your deck is a "tome or book" of these spells which is what the card back is supposed to look like. Having a library of books of spells.
Running out of spells in the game causes you to lose the game in Magic as well but in DBZ there were more common cards that allowed you to put discarded cards back into the life deck.