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If you have a powered repeater pointing into a block, the block itself is powered and powers any attached torches or adjacent powerable blocks (e.g. pistons, hoppers, glowstone lamps).

However if you have powered redstone dust pointing into the block, the block behaves differently. The block will still power attached torches or adjacent powerable blocks, but it will not power any redstone dust adjacent to the block (unless it's connected to the original redstone dust). Also, interestingly it will power a repeater coming out of the block.

So I've always wondered why is this? Is there a name for these two different concepts?

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You're experiencing the difference between "strong power" and "weak power".

Here's an illustration I made, in which green blocks are strongly powered, and yellow blocks are weakly powered:

Strong vs weak power image

Both strong and weak powered blocks will activate any adjacent mechanisms (pistons, lamps, noteblocks) and turn off torches attached to them.

The main difference is that weak powered blocks will not transmit power to adjacent redstone dust, although redstone repeaters/comparators can still "pull" power out of a weak powered block.

Blocks are weakly powered by redstone dust (either pointing into a block, or being on top of a block), and strongly powered by any other redstone component (button, lever, pressure plate, repeater, etc.).

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If a block has a powered repeater facing it, or a button, or another strong power source, it will be powered with strong power. If a block has strong power, it will be a power source. Redstone, repeater facing out, redstone on the block, all of that will be powered with signal strength 15. If powered redstone runs into the block, and it must face the block, not turn a corner next to it, then the block will have weak power. A weak powered block is partly a power source. Any redstone torches on it will be turned off, a repeater facing away from the block will be on, a redstone lamp on or next to the block will be powered, etc. However, a redstone signal will not pass through a block to another redstone signal.

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