Hard pulls you give your explicit permission to run do affect your credit. Soft pulls do not.
While hard pulls affect your score, they don't affect it much. Maybe a couple few point for a little while. In your daily activities, it is inconsequential. If you are prepping to get a mortgage, you should be mindful.
Similar type hard pulls in a certain time window will only count once, because it is assume you are shopping. For example, mortgage shopping will result in a lot of hard pulls, but if they are all done in a fortnight, they only count against once. (I believe the time window is actually a month, but I have always had two weeks in my head as the safe window.)
The reason soft pulls don't matter is because businesses typically won't make credit decisions based on them. A soft pull is so a business can find a list of people to make offers to, but that doesn't mean they ACTUALLY qualify. Only the information in a hard pull will tell them that. I don't know, but I suspect it is more along the lines of "give me everybody who is between 600 and 800 and lives in zip code 12344" not "what is series0ne's credit score?"
A hard pull will lower your score because of a scenario where you open up many many lines of credit in a short period of time. The credit scoring models assume (I am guessing) that you are going to implode. You are either attempting to cover obligations you can't handle, or you are about to create a bunch of obligations you can't handle.
Credit should be used as a convenient method of payment, not a source of wealth. As such, each credit line you open in a short time lowers the score. You are disincentivized to continue opening lines, and lenders at the end of your credit line opening spree will see you as riskier than the first.