Fun story...
By way of background, here in TX counties are by and large organizing distribution of the vaccines. Any TX resident who is eligible for the vaccine (anyone over 16 at this point, I think) can sign up on any or many wait lists and go to the first available appointment. You don't have to be a resident of the county distributing the shots in order to receive them there.
So I sign up for and receive my first shot of Pfizer (#teampfizer Woot! Woot!) in the next town over, sponsored by my county. I go in just a few days, maybe a week, before I'm scheduled for cardiac bypass surgery, with my surgeon's blessing. Schedule dose #2 for 3 weeks later, per protocol.
Surgery goes very well, and 3 weeks later I'm a couple of days out of the hospital and my second dose appointment is coming up. We're hearing all these potential side effects, and although every day is markedly better than the day before, I still had my sternum sawed in two and feel like I've been hit by a truck every time I sneeze. I'm still sleeping on the recliner, I'm still popping Norco at night. No big deal, but the doc says (reasonably imo) to hold off on dose #2. So I cancel, figuring there's a window and I can just reschedule again once the doc clears me for dose #2 in a few weeks.
Fast forward another couple of weeks, and I go to schedule dose #2. It turns out that the distribution center where I got the vaccine stopped using Pfizer and switched to Moderna (boo! hiss!). In fact, the original date that my second dose was scheduled was the very last day that they were distributing Pfizer. So they suggest I go to one of the other counties or distribution centers offering the Pfizer vaccine for dose #2. See online portal, yadda yadda yadda.
I call 3 different places around me that have Pfizer, and they all tell me that unless I got dose #1 with them, their protocol is to not allow me to schedule dose #2 with them. So I go back to the phone number of the original distribution center, who tells me that they've been hearing that from others, and they are just telling them to lie and say that they're signing up for dose #1. She's a city employee - she (a) is not a medical professional but assures me that the second dose is identical in every way to the first, and (b) has no phone numbers at the county, CDC, or anywhere else that can help me. Sorry, good luck.
I am able to confirm that this municipal employee can be trusted on this particular medical point, and both google and my cousin the physician are able to validate that, yes, the second dose is indeed identical in every way to the first dose. So, I lie and get the first (shh! actually second) dose from a different distribution center near me.
The only problem is that I now have two vaccination cards that both say I've been given dose #1. So in the future, if I have to prove to anyone that I'm fully vaccinated, I have to convince them that this is equivalent to getting both doses. I assume that, if society devolves into a dystopian hellscape, I will be relegated to the underground resistance as a result.
But at least I'll have a cool code name like "The Scorpion", and a plasma rail gun.
tl;dr: both doses are the same. Lying to the authorities for fun and profit.