請問在英文文法中有提到: provide sth for sb 但實際上在很多網站上寫的是: provide sth to sb, 網站上寫得對嗎? 為何要如此寫?

多數時候，provide something to/for someone 是沒有差別。
The agreement provided guarantees for union members when layoffs are considered.
https://www.ldoceonline.com/dictionary/provide

若要區分，則
The hotel provides a playroom for children. (消極地提供此一服務，不確定每位孩童都享用到此一服務)
We provide legal advice and services to our clients. (此一服務是直接提供與客戶，確保每一位客戶都接受到此一服務)
https://forum.wordreference.com/threads/provide-something-to-for-someone.3159977/

1.) If you provided umbrellas for your guests, that means that there is a supply of umbrellas available for their use.
2.) If you provided umbrellas to your guests, I would be more likely to assume they each have an umbrella in their hand.
https://english.stackexchange.com/questions/55925/preposition-with-verb-provide

附帶一提，to 普遍的使用是非常近期的現象，2000年後，有後來居上的趨勢。

※ provide something for somebody (為某人提供某物)、provide something to somebody (提供某物給某人)
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pro‧vide /prəˈvaɪd/ verb [transitive] 釋義-1. to give something to someone or make it available to them, because they need it or want it
# provide something for somebody 例. The hotel provides a shoe-cleaning service for guests.
# provide somebody with something 例. The project is designed to provide young people with work.
# provide something for/to somebody 例. The agreement provided guarantees for union members when layoffs are considered.
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provide [他動詞] 釋義-1.〈人に〉(必要・有用な物を)供給する，提供する，支給する，与える((with ...))；〈物を〉(人に)供給する，提供する((for，to ...))；…に(…を)装備する，備えつける((with ...))
例. provide children with a good education (子供たちによい教育を受けさせる)
例. Her prose provides us (with) a model of how to write. (彼女の文章は文章の書き方の手本になる) （◆((米)) では二重目的を取ることもある）.

我很懷疑一般文法書有可能把某一單字所有的用法都寫入。
provide sth to sb 我覺得用得很普遍，用to 有實際移動的意味
抄幾句英語系國家例句如下
1.What types of foreign aid does the U.S. provide to (免費提供 – 物資移動) other countries?
2.List four benefits that networks provide to (提供 – 服務移動到府) their users?
3.Provide medicine to children(提供藥物給小孩--物資移動) living with AIDS
4.Funding will help us provide books to schools (提供書本給學校--物資移動) we are working with, to children who don't have books and to many more schools in rural areas.
另provide with 也是一種用法
1. I need help. I don't get it. If possible, please provide with (提供) an answer.?

網站上寫的對嗎?
沒看到資料，當然不知，若是英語教學網站應不會出錯，像是本網站(例如我寫的 - 我英文不好)，還是要謹慎判斷