I haven’t dug into the method underlying your green card issuance time series, but recognize that green card holders (a) have 6 months to immigrate to the US, if not already in the US; and (b) very frequently are already in the US. I haven’t dug into the numbers, but in particular people coming off H1-Bs, refugees, people coming off spousal visas, people coming off victim of domestic violence visas, and parents of children born in the US, are all categories who will (or may) be in the US already. There are probably others, but those are the ones I can think of off the top of my head.
Accordingly, total volume over all time for green cards should be below total immigration, but there is a significant time window from issuance extending into the past (frequently over 10 years) in which a green card holder may have entered the US (and 6 months into the future). Don’t expect those time series to match up.