There are many different terms for housing configurations, and they can be used differently in different parts of the world.
In most English-speaking countries, housing is fundamentally described in terms of the number of bedrooms it has. In the New World, a listing will also indicate the number of bathrooms, e.g. an advertisement for a three-bedroom flat or a 2-bedroom, 1½-bathroom apartment. This is different, for example, from much of continental Europe, where you refer to the combined number of private and shared living quarters in a house. The kitchen, bathrooms, and any utility areas like a laundry room or storage room are not commonly counted in either case, but that varies a great deal by locale.
Bedroom simply refers to any room designated for private use, whether or not it is used for sleeping, in contrast to shared living areas like the living room, dining room, or recreation room. There may be legal requirements as to what can be designated a bedroom or not, according to local code, such as a minimum size or requirements for windows; converting the dining room in a 1-bedroom apartment into sleeping quarters does not legally render it a 2-bedroom apartment.
A unit which has only one common living and sleeping room could be called a zero-bedroom apartment or flat, but no one calls it that except some housing search websites. The conventional term would be a studio apartment or studio flat, or simply a studio if context is established that you are referring to the configuration of a living space.
This term originated in the U.S. in the late 19th century to describe a unit an artist or photographer might use both for living and working. This arrangement is, overall, quite rare in the U.S., even in major cities, and explains why suite is reserved for describing certain configurations of hotel rooms or student or monastic housing. Suite living is "normal" living, so saying you live in a suite would be redundant, and people will assume you are staying in a hotel suite or some other unusual accommodation.
Studio is not the only term in use, however. In the U.S., some distinguish an efficiency apartment from a studio, in that the kitchen in a studio is located in the main room, whereas in an efficiency it is segregated from the living/sleeping area. Others define the efficiency has having a only "kitchenette," whereas a conventional studio has full-sized kitchen appliances. Still others define one as being smaller than the other. The fact that the first four Google results on "efficiency vs. studio" all define them differently indicates that there is no consensus on the term.
Another term is bachelor apartment or bachelor (not to be confused with bachelor pad), although I sense this term is falling out of favor. The distinction between a bachelor and a studio is similarly nebulous, generally being that the unit is somewhat larger than an efficiency or studio, with a separate kitchen.
An alcove studio is a studio/efficiency/bachelor where the main room is laid out with an alcove (i.e. the floor plan has an "L" shape). So, while the unit is still one big room, one can have sleeping quarters in one wing of the "L" and living quarters in the other, for a greater degree of segregation than in a typical studio, but not as much as a full-scale one-bedroom unit.
Studio, efficiency, and bachelor all carry strong connotations of a small space, and so people will also use the term loft or loft studio or loft apartment for a very large single room. This term derives from the loft storage areas of factories, warehouses, or other industrial buildings that were converted for use as living space in New York City starting in the 1960s and 1970s. As musicians and artists were known for doing this, it became fashionable living, and nowadays, most "lofts" you see advertised are purpose-built rather than converted.
Suite living is "normal" living in the rich English-speaking world, and it is rare to encounter this term except when describing hotel rooms, student residence halls, and other unusual situations where you do not enjoy separate living and sleeping quarters. If you say you are staying in a suite, the assumption most will have is that you are staying in a multi-room unit in a hotel.
You may also encoutner references to en suite amenities, particularly a bathroom or closet. This refers to the fact that the bathroom or closet is accessible directly from a bedroom, as opposed to the hallway or other common area. This is somewhat confusing, but the idea is that the bathroom or closet thus becomes a private space, and it and the bedroom form a suite. Having a bedroom with an en suite bathroom does not mean you would describe your living situation as a suite, however, except in a very pedantic and literal sense.