What is the major difference between 层 and 楼？ I know that 层 can refer to other things like layers, etc. but I've heard that it could also refer to floors (just like 楼）。 Could I say something like "酒吧的第一层？“
层 is the measure word and
楼 is the noun being measured. They compliment each other and are not grammatically interchangeable, but the sentences you've heard are results from idiomatic omissions. There are two common situations:
1 . When we put 层 and 楼 together and an ordinal number before them, they form a noun phrase meaning
the N-th floor:
第三层楼 The third floor
This usage can be shortened into 第三层, 三层 or 三楼 (but not 第三楼). (第)三层 is fine for both formal and informal situations, while 三楼 sounds colloquial, otherwise they are completely interchangeable:
我家住在第三层楼 = 我家住在三层 = 我家住在三楼 = I live on the third floor (of a building).
酒吧在大厦的第三层楼 = 酒吧在大厦三层 = 酒吧在大厦三楼 = The bar is located on the third floor of the plaza.
2 . When we put 层 and 楼 together and a cardinal number before them, they form a noun phrase meaning
N stories and just like in English, this noun phrase is usually further composed into an adjective:
三层楼 Three stories (of a building)
三层楼高 Three-story high
Usages like this can be shortened into 三层, but not 三楼. E.g.
这个酒吧有三层楼 = 这个酒吧有三层 = This bar has three stories (is a three-story building).
这个酒吧有三楼 = There is a 'third-floor' in this bar. This sentence is valid but sounds very contextual, like an answer to questions such as 'I thought it's two-story high. Is there a 3rd floor?'
Examples for 三层高 (adj. phrase):
一栋三层楼高的建筑 = 一栋三层高的建筑 = A building that is three-story high.
On the other hand, 一栋三楼高的建筑 sounds unnatural.
If the subject of the sentence is literally '楼', then it must not be repeated. E.g. replacing '酒吧' and '建筑' with '楼' in above examples:
这栋楼有三层 = This building has three stories. (这栋楼有三层楼 sounds awkward.)
一栋三层高的楼 = A building that is three-story high. (一栋三层楼高的楼 sounds unnecessarily repetitive.)
Back to your question,
Could I say something like "酒吧的第一层？“
Yes. It means 'the first floor of the bar (which sounds like a multi-story building or occupies more than one floors in a building)'.
You might need to understand the mean of 層 and 樓.
樓 is a multi-storey building, usually wider than 塔. It is usually more than two floors. 樓 was rare in ancient China. There are some mentioned in poems like 岳陽樓 and 黃鶴樓.
層 is a storey of 樓 or 塔 and sometimes we say 層樓 or 一層樓. In an ancient poem, there are two lines of 欲窮千里目、更上一層樓.
When we counts storeys, we say 第一層, 第二層 and so on. Or 樓高六層.
The concept of 樓 for storey might be corrupted from 層樓. It is say 一樓, 二樓, 三樓 for location of floor.
You say "酒吧的第一層" is correct.