Question About Attack Rolls, Spell Attack Rolls, and Damage

[Prophet]

I'm having a hard time deciding on gear and understanding game mechanics. Can you all explain the difference:

Attack +1 = your chance to hit is increased by 1, effectively adding +1 to an attack roll.

1d4 bonus to attack rolls = a possibility of scoring a +1 to +4 chance to hit depending on the roll? So then, this is better than the Attack +1 above.

Do "attack rolls" affect spells that are based on "attack rolls," or do "attack rolls" only affect melee attacks, while spell attacks are based on "spell attack rolls"?

Obviously "spell attack rolls" only affect spells. Then, do "attack rolls" only affect melee?

Correct me if I'm wrong, but there is an attack roll, and then there is a separate damage roll, assuming you succeed in a successful attack?

[danielosky95]

there should be always something that lets you understand which type of attack the modifier it is referring to. like +1 to melee weapon attacks means only melee with a weapon and so on. If it says only attacks without specifing then it's all attacks, spells, melee, ranged, unarmed. For example the spell bless should apply to all types of attacks

An attack is in general when you roll a d20 to see if you are able to hit, the number to hit is the armor class of the target. Then depending on the weapon or the spell being used you roll a different die for the damage