Decaying are like coin tossers
It helps me to compare two different mental pictures.
The first picture, which is not at all like radioactive decay, is of lighting a fuse. It starts burning at the near end and burns toward the far end at some number of millimeters per second. Each section's chance of burning depends completely on the section before it: the second millimeter of fuse can't burn before the first one, and the third can't burn before the second, etc.
The second picture is a lottery based on coin flips. A billion people each have a coin to toss. Everyone who gets tails sits down, and the rest proceed to the second round of play. The last person standing wins the prize. Each person's chance of getting tails is completely independent of anyone else's toss, and every toss has a 50% chance of tails. You can expect that roughly half the people will sit down in each round. The actual number will be closest to 50% when the number of people is still large.
Atoms of radioactive isotopes are like the coin tossers. Each atom will decay at some random time, completely unaffected by what the others are doing. Of course, many rounds of "the radioactive decay lottery" are played per second, so instead of a coin toss you might imagine the atoms rolling a die with very many sides and sitting down if they get a "1". The more stable atoms have die with more sides, but each atom's moment of decay is still unpredictable.
Another way of stating a half life might be this: "given how unstable this isotope is, how long would you have to watch a given atom to have a 50% chance of seeing it decay?"
Just a repeated percentage change
I think a half-life pattern is just a convenient way of stating a recurring percentage decrease.
For example, what happens if you start with 1 million atoms and each year you lose 0.1% of whatever you have left?
I wrote a little computer program to simulate that. I had it run 10,000 rounds and print a message each time it reached a halving - that is, when the remaining amount reached 500,000 or less, then when it reached 250,000 or less, etc. Here's what I saw:
reached 499900.2346477281 at round 693 - 693 rounds elapsed
reached 249900.24460085342 at round 1386 - 693 rounds elapsed
reached 124925.1909144911 at round 2079 - 693 rounds elapsed
reached 62450.132251566276 at round 2772 - 693 rounds elapsed
reached 31218.83576633967 at round 3465 - 693 rounds elapsed
reached 15606.30332502206 at round 4158 - 693 rounds elapsed
reached 7801.594694162155 at round 4851 - 693 rounds elapsed
reached 3900.019018238128 at round 5544 - 693 rounds elapsed
reached 1949.6204223478458 at round 6237 - 693 rounds elapsed
reached 974.6157066056886 at round 6930 - 693 rounds elapsed
reached 487.2106204235443 at round 7623 - 693 rounds elapsed
reached 243.55670347259502 at round 8316 - 693 rounds elapsed
reached 121.75405321597741 at round 9009 - 693 rounds elapsed
reached 60.864879771978956 at round 9702 - 693 rounds elapsed
So every 693 rounds, the amount halves. This remains consistent after 10,000 rounds and after 1,000,000 rounds. (Eventually it breaks down, probably because the program has limited mathematical precision.)
If I have it lose 2% each round instead of 0.1%, the half-life is 35 rounds.
Based on this, I think you could state any half life in terms of percentage loss over a period of time. But "percentage loss per year" would hardly make sense for isotopes whose half life is a fraction of a second, and "percentage loss per second" would be incredibly small for isotopes with a half life in the billions of years. Speaking in terms of half lives gives us a single number to compare between those two isotopes.