Consider the following:
- Filipino (register) is a standardized register/dialect of Tagalog (language).
Meaning, there are other, non-standard, dialects of Tagalog.
- Tagalog (language) is the native language of Tagalog (ethnic group)
- Tagalog (people) are one of many ethnic groups in Philippines (country).
There are other ethnic groups who have their own languages, and some of these languages are also official/regional in the country.
Hence, a text can be written in Filipino, while verbal services (e.g., phone support) is in Tagalog (assuming that the Web site does not support any other language of Philippines).
Here's yet another view of the problem:
In practical terms, Filipino is the official name of Tagalog, or even a synonym of it. Today's Filipino language is best described as "Tagalog-based".
Use of term Filipino in this context is a metalepsis which suggests metaphorically that that the national language is based on an amalgam of Philippine languages rather than on Tagalog alone.
The language is usually called Tagalog within the Philippines and among Filipinos to differentiate it from other Philippine languages, but it has also come to be known as Filipino to differentiate it from the languages of other countries; the former implies a regional origin, the latter a national. — Wikipedia — Filipino language — Filipino v. Tagalog)
As per Chinese, 中文
[zhōng wén] may be preferred versus 汉语
This question seems to be relevant:
中文 vs. 汉语: What's the difference?