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 from the address to another address and
100i from the address to yet another address.
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.
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
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.