This problem came to my mind when I saw ads on YT. In my native language (those two words are derived from English and have exactly the same spellings), we might use both (equally) to say:
The video is supported/sponsored by X.
X is a product and could be anything like shampoo, drinks, food, etc. I believe those two have different meaning.
The word support have 6 senses according to CALD i.e. encourage, help, provide, stop from falling, prove, and accept. However, CALD also defines the verb sponsor to support a person, organization, or activity by giving money, encouragement, or other help. It's perplexing and paradoxical.
Are these terms interchangeable?
My reason I'm asking this question is because someone corrected me when I commented this video is supported by X and suggested sponsored by instead. From here, I'm questioning the difference.
Best Answer
In the context you describe (YT video sponsorship/support) they have different connotations.
"Sponsored by" suggests that the entity doing the sponsoring has paid the full cost. They are primarily responsible.
"Supported by" suggests less involvement. They approve, may have provided some financial support, but are not as directly involved.