Is a 20 strength weapon with a special ability of +10 attack the same as a 30 strength weapon in Breath of the Wild?
According to posts here, that number is actually included in the weapon's attack stat. A 20 strength weapon with an Attack Up +10 modifier indicates that the weapon has a base attack stat of 10, but was raised to 20 with the modifier.
The total value (white number) includes the bonus you see.
The number includes the added attack. If you have a weapon with 45 attack and "+15 mod", the original weapon value is 30.
Thus, if you're looking at a weapon that has 20 Attack but has an Attack Up +10 modifier, then that weapon really does have just 20 Attack, because its base Attack was actually 10.
If you meant that that weapon normally has 20 Attack, but you're asking about the theoretical situation where it has an Attack Up +10 modifier, then yes, that weapon would be equivalent to a 30 Attack weapon with no damage modifiers.
Yes, you can consider them to be equivalent. In the inventory screen, weapons with Attack Up and shields with Guard Up have higher numbers than other weapons/shields of the same type.
This is especially easy to test with weapons - if it normally takes (as an example) about 5 hits to kill an enemy with weapon X, it might take only 3 or 4 hits with an Attack Up weapon of the same type. (You can also use the hero shirt to verify how much damage you do to enemies.)