Seeing through Chapter 10: Spellcasting, 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:
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?
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:
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 -