What is the difference between 东西 and 用品? They both seem to have the meaning "stuff" in certain circumstances, but then 用品 is used in more formal situations, such as 医药用品 which I am assuming is not in the same register as if I were to say "Pharmaceutical Stuff"! I lean towards translating 医药用品 as "Pharmaceutical Products", but I am not convinced that 用品 is really the same as English "product".
用品 is used for articles that can be used, articles for use (Definitions is 2 dictionaries: 应用的物品 / 供使用的物品).
- 办公用品: Office supplies, office goods
- 日用品: articles for daily use
- 常用品: everyday implement; object of everyday use
- 床上用品: bedclothes; bedding
- 体育用品: sporting goods
- 教学用品: educational supplies, study material
东西 is just a thing.
You should contrast 用品 with 产品. 产品 is something that is produced/manufactured, hence a product (Definitions in 2 dictionaries: 生产出来的物品 / 劳动所创造的物质资料，包括生产资料和消费资料). The last dictionary says it's also used for consumer goods.
So for 用品 the emphasis is more on the usage, and for 产品 it is more on the production.
用品 refers to articles of utility.用 = use, 品= articles. That is things that are used in well defined contexts, per BertR's answer.
东西literally means "east-west." Figuratively, it refers to "random" items.
用品 is much more formal than 东西. I use phrases like 工作用的东西，开车用的东西，学习用的东西，etc., quite often in when speaking, but almost never when writing Chinese.
First ,you might know the origin meanings of '东西'. The Chinese word '东西' origins from '东市' (East Market) and '西市' (West Market) in Tang Dynasty. At that time, people bought stuff in the East Market or West market (人们去东市或西市买用品). After years, people simplified the usage and used the word '东西' as '用品'. For example, '人们去买东西'.
Nowadays,东西 is used often in talking with people. '用品' is used in writing articles. But you should not add a 'noun' modifier before '东西'. For example, '办公东西' is not used in China.