I unfortunately had an overdraft on my checking account and my bank transferred money from a reserve line. Will this affect my credit score? Or is it independent from that?
You won't get reported to a credit bureau for an overdraft, that's a service offered internal to the bank. The only way it would affect your credit score is if you had an overdraft fee that you didn't pay, which would get reported.
There's is a system that gets a notice when you overdraft though. The bank MIGHT report you to ChexSystems, which is an agency that tracks the mishandling of accounts. Generally, a fee based overdraft is an agreement with you and the bank that they will charge you a fee, this is desirable to the bank, so they don't report to ChexSystems unless there's some sort of abuse. Banks view overdraft like a product for revenue generation and they encourage you to continue. Examples of abuse are: intentional overdrawing where the bank updates the account balances by batch jobs, so that you can overdraft 5x$1000 on an account that only has $1000+fees in it. Banks check ChexSystems to see if you have mishandled accounts to determine if you can open up another account, though they're mostly checking to see if you are leaving accounts in bad or negative status.
Your credit-score is concerned with your current credit accounts (credit-cards, HELOC, loans, mortgage, et cetera) - your Current/Checking bank account is not a credit account so it is not reported to the credit agencies.
Granted, being overdrawn is effectively the same as having a very expensive loan from the bank- however banks do not routinely report these to the credit-agencies - and of course, if you fail to pay overdraft fees in a timely manner then your bank will take it to collections or possibly even get a judgement against you, and that will be reported in your credit report (under the "Derogatory remarks" section).
I cannot find any sources as to whether repeated but always-paid overdrafts will be reported - but certainly your bank isn't complaining because they'll be making lots of money from you.