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Seeing through Chapter 10: Spellcasting, Attack Rolls:

Attack Rolls
Some spells require the caster to make an attack roll to determine whether the spell effect hits the intended target. Your attack bonus with a spell attack equals your spellcasting ability modifier + your proficiency bonus.

Most spells that require attack rolls involve ranged attacks. Remember that you have disadvantage on a ranged attack roll if you are within 5 feet of a hostile creature that can see you and that isn’t incapacitated (see chapter 9).

The bold part makes me belive that, when I cast a spell, I should add to the damage my proficiency bonus + my spellcasting ability modifier. It makes sense. The more proficiency and ability modifier I have, more powerfull my spells should become.

But, looking at Chapter 9: Combat, Making an Attack:

Attack Rolls
...
MODIFIERS TO THE ROLL
When a character makes an attack roll, the two most common modifiers to the roll are an ability modifier and the character’s proficiency bonus. When a monster makes an attack roll, it uses whatever modifier is provided in its stat block.

Ability Modifier. The ability modifier used for a melee weapon attack is Strength, and the ability modifier used for a ranged weapon attack is Dexterity. Weapons that have the finesse or thrown property break this rule. Some spells also require an attack roll. The ability modifier used for a spell attack depends on the spellcasting ability of the spellcaster, as explained in chapter 10.

Proficiency Bonus. You add your proficiency bonus to your attack roll when you attack using a weapon with which you have proficiency, as well as w hen you attack with a spell.

The bold is talking about using the modifier - and after sum the proficiency too - to the attack roll.

So, my question is...
Are they talking about two separate things, and proficiency and ability modifiers(Charisma, in my case) are used both in damage and attack rolls, or is it only to attack rolls?

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No, you do not add your spell-casting ability modifier to a spell's damage roll unless it is specified in the spell description. From chapter 9, page 196:

Damage Rolls: [...] When attacking with a weapon, you add your ability modifier - the same modifier you used for the attack roll - to the damage. A spell tells you which dice to roll for damage and whether to add any modifiers.

Modifying this rule would also undermine class specific abilities, such as the Warlock's Agonising Blast Invocation.

With regards to understanding the specific terminology you have highlighted -

  • The spell attack roll, as outlined in the rules quotation you gave, only acts to "determine whether the spell effect hits the intended target" with any subsequent damage dictated by the spell description.
  • The attack roll is 1d20 + the attack bonus.
  • The attack bonus is equal to your spellcasting ability modifier + your proficiency bonus.
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  • \$\begingroup\$ Thanks. Since I'm using the Portuguese(Brazilian) version, I need to double check if it is a mistranslation or that I misunderstood. Thanks for the clarification. \$\endgroup\$ – klauskpm Feb 20 '17 at 14:48
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    \$\begingroup\$ @klauskpm It might be worth mentioning that in future questions, actually -- knowing that you are mostly working from a translated version of the rules might stop people from assuming you just didn't read the rules at all. \$\endgroup\$ – Marq Feb 20 '17 at 15:17

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