No, there's a huge difference. The difference here is that the Manufacturers and the Carriers are gatekeepers to the customer's phones.
The manufacturer made customizations to Android for their phone. Android isn't a cleanly-separated stack where the manufacturer modifies only a certain part of the stack for their phone but Google could go and update another part without risk of breaking anything (is any software project?)
Then, the manufacturers sell the phones to carriers, who usually request extra customizations to (at best) add their logo, or replace default apps with the carrier's own version. This means that any updates to Android likely require updates to this customization.
But even if that customization was free (from a development perspective), Carriers still have maintenance/service contracts with the manufacturers such that any manufacturer's updates must go through the carrier's "quality control" procedure. You wouldn't want an update to make the, say, LTE radio misbehave and break the carrier's network would you? Oh no... (and you certainly wouldn't want to "forget" to replace the good default app with the Carrier's crappy one)
So there you go, a quick glimpse into the complex economic/contractual obligations that delays or blocks Android updates. FWIW, Google has been working both technically and contractually to untangle this mess, and is one reason for the existence of their "own" line of Nexus and now Pixel phones.