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As far as I understood:

double-spending: is when you do a second outgoing transaction while another one is still in pending. (this is possible only with Android wallet, because the light wallet [computer] has a protection [called key-reuse])

address-reuse: is when I send iota to and address that was used to send OUT iota. Usually those addresses are strikethrough on the wallet and with a red icon.

If this is correct, which of those two action will affect the security of the seed? If both, which one is worst? And how does it works?

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Every double-spending is an address reuse but not every address-reuse is a double-spending.

Let's say you have an address with a balance of 100i

Double Spend

You send 100i from the address to another address and 100i from the address to yet another address.
or
You send 40i to from the address to another address and 70i from the address to yet another address.

Both are double-spends (because you spend more money than you have) and both are address-reuses because you send twice from the same address therefore you have to sign twice with the same private key.

Address Reuse

You send 70i from the address to anoher address and 30i from the address to yet another address.

This is not a double spend because you don't spend any IOTAs twice. You spend exactly 100i and you have exactly 100i.
Nevertheless it's still an address-reuse because you spend twice from the same address therefore you have to sign twice with the same private key.

Security of your seed

No matter how many double-spends you do, the security of you seed does not get compromised. What does get compromised is the private key of that address.

Private/Secret keys are generated from your seed. A Public key (=address) is generated from the private key. Every address has a private key.

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    this is a complete and well done answer. Maybe it's not here the place to discuss this, but I'd like to know how this private key compromisation works. Let's say, I compromised the private key somehow doing a transaction. This transaction was taking money from 2 of my addresses (in the tangle explorer under IN) to send to another address (OUT). Is the private key of both addresses compromised or only for one?
    – overkill22
    Dec 7, 2017 at 12:08
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    Every address the transaction is "taking money from" gets exposed to some extent. For details take a look at "iota.stackexchange.com/questions/245/…" and "iota.stackexchange.com/questions/467/…" or ask a new question
    – Zauz
    Dec 7, 2017 at 16:09
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The action that will compromise your security is sending a transaction from the same address twice.

That is what address reuse is: sending a transaction from the same address twice.

You CAN do this by double spending, which is trying to send the same IOTA multiple times while it is still pending. But you can also re-use your address by sending, receiving at the same address, and sending again, all without truly trying to do a double-spend.

Double spending in itself isn't inherently dangerous to your seed.

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