What you want to find is " multi point capable" with "a2dp" .
The multi point is pairing to 2 devices at once, though only 1 can be connected at a time and the a2dp is the Bluetooth profile that allows music and podcasts to play thru it. Both the iPad and iPhone support a2dp already.
Without knowing what type you want I won't suggest anything specific because there are way too many models to choose from of differing styles. I use a Jawbone Icon on my phone and iPad
The way my icon works is I'm listening to music on one device, get a call on the other, tap the button and it switches devices it's connected to. I write devices because I have Whistle on my iPad for phone calls via VoIP and can make calls or receive on my phone or iPad.
Fwiw and a bit off topic I also have TextNow for texting and PassItForward on my phone to forward texts from my phone to my iPad
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