Similarities and differences
First, let's check Yoda and Maz Kanata's similarities and differences:
Yoda has green skin and Maz Kanata has yellow-brown. Not very different but also not similar. Explainable by racial or ethnic differences.
Yoda has a bit more than half the height of Maz Kanata. (66 cm vs 124 cm, according to Wookieepedia). A big difference, which suggests that they are not the same species. However, if their species are the same, this could be explained by a high genetic variability (just as happens to real-world dogs) or if at least one of them has an abnormal height.
Yoda features big pointy ears, which is not something we see in Maz Kanata. This strongly points that they are not the same species.
Yoda has a few hairs. Maz Kanata seems to have no hair whatsoever. This tells us nothing at all between them, just tells us that they are unrelated to wookiees or ewoks, which is no surprise.
Yoda has three fingers on each hand with long pointy nails, while Maz Kanata has four fingers on her hands. I can't see clearly if Maz Kanata has no nails or very small and thin nails, but either way, it is very different than Yoda. This also suggests that they are not the same species.
They both use some unusual word order and phrase structure when talking English, which implies that it is not the native language of either. However, their word order and phrase structure are also very different from one to the other, so they should also have different native languages.
Their faces have similar positions, size and format for eyes, nose, mouth and forehead wrinkles, which suggests that they are the same species or at least somewhat related.
They are both similarly very long lived, suggesting that they are from the same species or at least from related species.
Both of them have an mysterious/unrevealed/undisclosed origin.
There is also Yaddle who is a female from Yoda's species and very similar to Yoda. Wookieepedia's article also cites a few other members, called Minch, Oteg, Vandar Tokare and somebody else who is shown as a statue and is unidentified. However, many of those could not be considering canonical in any way after Disney's great purge, but the fact that they are all very similar to Yoda and very distant to Maz Kanata strongly suggests that Maz Kanata is unrelated. Also, it seems that all of them are Jedi, and Maz Kanata is not a Jedi.
Well, so in the end the answer is a simple and deceptive "we don't know and have no way to know for sure".
However, with that I can propose two theories:
Theory A: They projected Maz Kanata simply to make the fans remember about Yoda because she might take a similar role in the plot, but it is no more than that.
Theory B: Maz Kanata was projected with the intention of making its relation to Yoda unclear, by intentionally showing both similarities and differences. Maz Kanata was made in a way to be similar, but not too similar to Yoda, and this is on purpose, not an accident or a coincidence.
If we go on with the theory B, then it would be too deceptive to the fans if in the end they just have no relationship whatsoever, and in this case they should be related somehow. Also, the facts 8 and 9 above suggests that the theory A is false. If my theory B is in fact correct, Disney will exploit their similarities and differences somehow in the following movies, as a way to add mystery and fan-addictiveness to the plot, something that J.J.Abrams know how to do very well.
With that, if the answer is simply "they are unrelated", Disney would be deceiving fan expectations and losing an opportunity to add more mystery, expectation and addictiveness to the plot. So the truth must be one of the following:
A) Related, but different species (like a lion and a tiger).
B) The same species, but very different races or ethnicity.
C) The same species, but featuring a great genetic variability (like dogs).
D) The same species, but featuring sexual dimorphism. [Nope, Yaddle was a female from the same species very similar to Yoda]
E) The same species, but at least one of them is a very abnormal individual within the species.
From the telegraph site:
Abrams and Nyong’o acted as intergalactic cupids at a press conference ahead of the film, after actress and comedian Mindy Kaling asked the latter: “Can you talk about your character's relationship with Yoda?”
Abrams replied: “I do believe that Maz and Yoda at one point had crossed paths. But that is not something, of course, due to the events of past films, that happens in this one."
Nyong’o added, as a joke: “he was my first love”.
But there may be more evidence to it than a light-hearted comment. Romantically inclined fans have hypothesised that Maz (who has since moved on to Wookees[sic]) inspired the ban on Jedi having romantic relationships (see Anakin’s cringe-worthy quandary in Episodes two and three) after a rendezvous with Yoda.
One Reddit user even went as far to suggest that Yoda “impregnated” Maz with Snoke, after “loneliness, senility and despair” entered his mind at the end of Episode III. Obviously, many people laughed at this.
In my interpretation, I think that they purposely didn't give any useful information and instead fled from the question.
Also, from this article on ew:
What kind of species is she? What is her homeworld? “All that backstory will be forthcoming,” Abrams says. “In the movie, you don’t learn these things, but I know that these are things that are coming out in other venues.” So keep your own eyes out for more of Maz’s past to be fleshed out in books or games.
For me, this looks like a direct refusal in answering that. Which shows that he is hiding something interesting on purpose.
What about Yoda's origin?
Independent from what is or not Maz Kanata, will Yoda's origin be revealed?
The answer is simple that we don't know. But some rumors say that yes:
While Rogue One will be a war film and the 2018 film will be a western, the third Anthology film will be much more 'mythological and spiritual' based. While it was once reported that a Mace Windu movie may be in the works, there's been strong speculation that this could be an origin story regarding Yoda. While the backstory of Yoda has been a closely guarded secret for some time it seems, the fact that this would be a possible final Anthology film, is an interesting notion."
Either way, this is still an unconfirmed rumor at this time so nothing is set in stone.