謝る and 感謝する: apology and gratitude
Distinguish the fault apologized for from the help appreciated.
Apologizing for a fault
謝る (あやまる) means apologizing for a fault or inconvenience. 「遅れたことを友達に謝りました」 says that the speaker apologized to a friend for being late. を marks the matter and に the recipient.
「謝るつもりです」 expresses an intention to apologize. Unlike reporting a completed apology, it does not establish that the other person has received one.
Being grateful for help
感謝 (かんしゃ) means gratitude, with 感謝する as its verb. 「友達の助けに感謝しています」 expresses gratitude for a friend's help. に can follow a person, but here it marks the help being appreciated.
「感謝の気持ちを伝えました」 says that gratitude was conveyed. Distinguish feeling grateful from communicating it through words or actions.
Reading the function in context
「すみません」 can express gratitude and indebtedness after receiving help, as well as apology. Do not assume an admission of fault from the expression alone; check what it responds to.
「迷惑をかけてすみません」 apologizes for causing trouble, while 「助けてくれてありがとう」 thanks someone for helping. Adding a reason clarifies the function of the response.
What happened first in 「謝ったので、許してもらえました」?
Show the answer and why
The apology came first, and the speaker was forgiven as a result. Keep the apologizer and the person granting forgiveness distinct.