There was a similar question not long ago; I copied my answer (with some reference to the OP's unique spin on the question), presenting it here so as to avoid having to follow a link:

The simplest answer is that religion and mythology are "different concepts that are strongly linked together" as you ask, but simple only gives a simple answer.

Part of the problem revolves around the modern use of the word "religion": what that term conjures in the modern mind does not necessarily fit what was going on in pre-conversion European cultures. And what was going on in those cultures depended a great deal on the culture and on whether we are talking about sophisticated urban writers or dirt-under-the-fingernails people in the field. And of course, things were very different in Archaic Greece as opposed to the Hellenistic world of Alexander: everything changes over time (and place).

It is probably good to think about belief systems, ritual practices, and traditional stories about the supernatural. Virtually all cultures have belief systems about some aspect of the supernatural (although /r/anthropology is fond of debates about whether this or that exception really is the exception). People have always tended to believe that the world is filled with supernatural forces and/or entities, and they have pondered how to interact with the supernatural, whether they can influence the supernatural and what they should do to protect themselves from the supernatural.

That leads us to ritual practices. Again, most cultures have a set of ritual practices that provide a means to protect from and otherwise show respect for and/or protect people from the supernatural. Ancient urban cultures tended to have formally designated professionals (priests and others) who were in charge of directing those efforts or at least of handling them for the society as a whole. This structure can lean toward feeling like a religion in the modern sense, but sometimes these were simply things that needed to be done to maintain balance and many people may have remotely taken solace in the idea that things were being handled, but it does not mean that they had a level of personal devotion, ecstasy, and interaction with supernatural beings in a way that we see in modern religion.

In fact, part of the problem in looking back with modern terms and concepts as our cultural baggage is in the term god/gods: the modern God as an omnipotent, omniscient alpha-and-omega type Guy is largely absent in ancient "religions." Their gods had limits. They were powerful supernatural beings - some more powerful than others, and many powerful only in this or that lake or river, or forest, or tree, all in the most immediate and local sense. These aren't like the modern God. They were limited and fickle, and they often required ritual to be placated, manipulated, and/or distracted. Not very God-like; and not very religion-like.

Then there are the traditional stories that were told. Many were told to be believed, but some may not have been. Some were narratives about culture heroes and even about events within historic or near-historic times. Others explained the origin of the world or the origins of specific things in some remote primordial setting. But all of these stories tended to have the supernatural as a thread or even as a general woven aspect of the tapestry. They gave illustration about how the supernatural behaved, what it was like, how it influenced the nature of the world, and how the supernatural forces could affect everyday lives. The stories gave illustration as to why the belief system was valid, and they often explained why the rituals were needed. At the same time these narratives provided a cultural net of ethics, values, and basic structure for society. These narratives - what we refer to as mythology - were expressions of beliefs and rituals that we rightly or wrongly describe as ancient religion, but that link is tenuous and if applied too strongly, it breaks.