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I am applying to math REUs in the United States, which require letters of recommendation. I wanted to ask my faculty advisor for the letter - I get along well with them, they have seen my progress over my entire college career so far, I ask them fairly many questions about graduate school, and they were able to get me a grant to attend a math conference. They are also professor emeritus at my college.

However, I haven't dealt in real math with them, in the sense that I haven't been taught by them or done research with them.

Thus, while my advisor would write me a good letter, I think it would not be from the standpoint from someone who has directly witnessed my mathematical skill?

I am planning on sending one letter from a professor who has taught me in an intensive course. Is it a good idea to ask my advisor for the second letter, or should I ask a professor who has taught me instead?

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Having been in the writer's position, I would say the most important thing is whether I know anything concrete that I can cite in support of any statements I make about your character and abilities.

Although having taught someone definitely helps furnish such concrete examples, it's neither necessary nor even sufficient. It depends more on whether the person has distinguished themselves at all and done so in a way I can be aware of. If it's just about grades I don't need to have taught you to consult those. But if it's about whether you show leadership and initiative, I might have seen that in class or I might have seen or heard about that outside of class.

Once a student asked me for a recommendation for an engineering program after I had taught her English. We had a good relationship, but of course my perspective was limited. So I spoke personally to the qualities I had seen that would serve her in any program, and then I asked others who had taught her whether she had distinguished herself in their courses or outside them. Another student provided a resume and answered my questions about things on there that I thought I might want to reference.

Your advisor, if they have watched your progress throughout your career, probably has a lot of concrete things to say about you. But in any case, they'll be able to judge, and there's no harm in asking (and even acknowledging that you understand that they might not be able to).

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You should always ask for a LOR from a faculty member who knows you well.

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I'll guess that such a letter would be fine. After all, they are in a position to gather information from their colleagues who have taught you and can write a nice "summary" letter if they so choose.

They certainly seem to be supportive. I don't see a downside, given the other things you say.

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