Yes, it's related to (in that it's often a beneficial result of) but it's not explicitly the same as DevOps, by any definition I've seen, good or bad.
I've been discussing this with others in the "DevOps" space and in recruiting terms a "DevOps engineer" seems to mostly mean an "Ops engineer". True Devops (in the sense of developers who also care about and perform all of their own operations) is a culture, not a job role and one that seems quite rare in the wild.
Look up Jez Humble for a bit more idea into the origins of the term. The term is a primarily a buzzword among larger companies and almost always followed up by some engineering cultural change objective rather than about how code is deployed or even developed and run. You know that it's another management-focused trend when there's entire conferences where people say devops constantly without mentioning anything about code and half the folks in attendance or speaking are consultants in suits that consider Excel formulas the extent of their coding skills.
So the common theme I see is "any way besides what we used to do operations traditionally." It's mostly used for "operations with some idea of what is being deployed on the stack above them." Most start-ups don't have this problem at all with modern infrastructure (no more rack and stack at your 5-man start-up probably) though by definition because rigidly defined roles are a Big Company Problem.
"Modern" infrastructure (by which I assume you mean provisioned, destroyable VPS instances + associated services such as AWS, Azure, etc) is effectively just a new "how" - you call an API instead of deploying a config file or similar. You still need to know the "what" and the "why" to be effective.
I'm being very conservative with what "modern" means (within the past 20 years is about right). Traditional shops are still racking and stacking machines and maybe deploying VMs by hand using ITIL stuff trying desperately to slow down system changes to deal with demand rather than to speed things up like most shops have done. Where I am now, the "traditional" IT side of the house takes roughly 5 months to provision a new server (I lead operations on anything bleeding edge, which is now standard for most start-ups).
Going from using maybe kickstart files to API calls is not as big of a deal as the fact that you can even get something on demand in any way instead of going, finding another job, quitting that job, coming back in shame, and realizing that the server you asked for is finally up.
As I said, I don't treat "developers can push to an environment" to be the defining factor or the definition of devops
Historically large companies had strictly separate development and ops teams. DevOps is about fusing them together so they talk to each other and influence each other's thinking for the benefit of everyone.
But of course sane definitions don't make good buzzwords so now we hire "DevOps" people just like we buy "private cloud" servers.
DevOps is as much about making your developers ops engineers as Agile is about making your stakeholders developers. It's a possible side-effect, but neither necessary nor sufficient.