Well, that is a quite complex question. Mainly because different disciplines use the words in different ways and some people indistinctively. Theoretically, the habitat (form Latin Habitare, live in or dwell) is a place (or the area including all such places) that offers a species resources required to fulfil its life-cycle (food, shelter, reproduction). Thus habitat is a species-specific term. And from the perspective of a species all the landscape is a matrix of habitat or non-habitat (depending of it can live in there or not).
The term niche is broader and also related to the position a species occupy within the community. Therefore, the niche encompasses not only the habitat (the species can live or not in there) but its position in the tropic chain, interactions with biotic and abiotic characteristics…), There are two different “concepts” of niche, one is something like definite boxes occupying the spectrum of available positions. We could have something like “big size insect eating bird” “medium size insect eating bird” “small size insect eating bird” ,“Big size seed eating bird”… and so on, with the possibility of finer detail in sizes and food spectrum. You can see this idea better developed in Elton´s classic book “Animal Ecology”. The other concept is Hutchinson´s hypervolume. There the niche is views as the hypervolume defined by resources and conditions that allow for the existence of the species. From that point of view, the habitat could maybe be defined as the area of land where the conditions of the hypervolume (or at least the resources and basic requirements) are present.
Ar some point, probably based on some large species inhabiting them, or their typical communities, people started referring as “habitats” to more or less uniform vegetation formations, although they may only part of the “habitat” of some species and only partially the habitat of some others. That term got a strong grab in society and nowadays we have things like “habitat maps”, “habitat conservation and management” that can imply very different things depending on what each ones considers a “habitat” to be.
My suggestion is that if you are to use any of the terms, at some point state clearly what you mean and provide a brief definition.
A nice involves interactions with other organisms, but there isn't a grand consensus if all interspecific interactions (such as facilitation) are included in the niche. A recent post about this from Meghan Duffy covers this ground well, and the comments are useful too:
While habitat is a suitable place for an organism to live, I like to think about niche in terms of an hypervolumetric dimension, that encompasses all conditions and resources an organism can live in. Say, for example, that you have a 2 dimension graph that encompasses, for example, diet and salinity. Those are certainly not the only conditions and resources an organism necessitates to survive. Then, you add a third axes that is related, say, to pH, and there you'll have a 3 dimensional graph (therefore, you will have a volume) that still do not emcompasses all the necessities the said organism needs to survive. Now, if you keep adding axis (temperature, humidity, oxygen disponibility, etc.) you will have a graph with n dimensions that is called the HYPERvolume, because it has more than 3 dimensions (therefore, it is more than a volume, it is an hypervolume). The sum of all of these dimensions will end up encompassing all the conditions necessary to an organim to surviva. That is why the definition of niche is often referred as an hypervolumetric niche. If you need more explanations, I suggest reading the ecology book from Michael Begon - there is a whole chapter that deals only with niche dimensions!
A niche refers to the way in which an organism fits into an ecological community or ecosystem. Through the process of natural selection, a niche is the evolutionary result of a species’ morphological (morphology refers to an organism’s physical structure), physiological, and behavioral adaptations to its surroundings. A habitat is the actual location in the environment where an organism lives and consists of all the physical and biological resources available to a species. The collection of all the habitat areas of a species constitutes its geographic range.
The point of view on different terms are usually different for different researchers. In my opinion, the area is a set off the places where the species exists; habitat is a place where the population exists; niche is the set of conditions in which the population can survive.