I'm starting to feel like I'm letting this friend down because I can't be what she wants me to be

Op ~ what you're probably being is disingenuous
Something you have done has given her this impression, this impression of BFFs. Maybe you give a lot for short periods
(and then cool-off which makes you feel guilty) Try to even out the contact. How often to you want to see her, talk to her?
You decide. But when you are together, give of yourself, all-in when you are together. If you can't do that, she needs to
know you aren't really a friend to her. And never beg-off on plans with her w/the excuse of being overwhelmed,
sick, stressed or under some emotional turmoil - this is unfair. Unfair because a good person will feel sorry for you and
think, more than ever, you need a friend to stick by you. It makes the relationship even further lopsided. And is just cruel.

If you are letting her down because you are very busy with your own life then that is her issue to deal with, not yours. You can graciously and kindly decline her invitations when it's not doable for you and maintain the frequency of texting/calls that is comfortable for you. I barely see my close friends because we're all so busy but it's more about the quality than the quantity of time that we spend together. She'll eventually adjust and if she doesn't, there's nothing you can do. Hopefully she'll continue to enjoy your connection despite the fact that you're not as available to communicate and socialize with as she is.

I'm not sure what the issue is? Why does it bother you that she thinks of you as a best friend? Are you one of those people that can only have 1 best friend.

You don't need to tell her that although you are her best friend she is not yours.

It is OK to set boundaries, though, and set aside an amount of time every day/week for her rather than being at her beck and call.

Sounds like she has mommy issues

You sound like a child with this BFF bullshit.

One rule of adult friendships is that your BFF might not see you as her BFF. And that's okay. Maybe you ARE the wind beneath her wings. If so, you're a good person to support her. Maintain appropriate boundaries for your mental health, but don't devalue the friendship in her eyes.

Not replying to her texts or calling her every week will the right message.

I have a very sweet friend who I like a lot. She's significantly younger than me but we have a lot in common. The problem is, she thinks we are best friends. She texts me about literally everything that happens in her life. She is constantly telling me how greatful she is for our friendship, and how she doesn't know what she would do without me. She has other friends, and she is not in constant communication with them like she is me. Unfortunately I am extremely busy and my time is stretched thin as it is. I can't text her everyday or talk on the phone every week, or plan the next get together as frequently as she would like. I feel like there is no polite way to say, "yes we are friends but you are not my best friend." I have best friends who I rarely get to see because of how busy we all are and I'm starting to feel like I'm letting this friend down because I can't be what she wants me to be.