The difference is what each one can physically hear.

Your phone records its microphone. It hears the room: you, and anyone in it with you.

Your laptop records its microphone and everything coming out of its speakers. It hears you and the people on the call, because their voices arrive through the computer.

SituationUse
Video call on Zoom, Teams or MeetLaptop
In-person meeting or interviewEither; phone is easier
Conversation in a corridor, taxi, or on sitePhone
Phone call on speakerphonePhone, with the caveat below
Phone call held to your earNeither, reliably
Somewhere with no signalPhone
You want a transcript as it happensLaptop
You want to ask Junior questions mid-callLaptop

The one that catches people

Recording a video call on your phone captures your side of it clearly and the other side barely, or not at all. Their voices are coming out of your laptop, on the other side of the desk. It looks like it worked, because the timer ran and the waveform moved. Use the laptop for anything on the laptop.

Questions

Can I record a phone call?

On speakerphone, usually yes. Held to your ear, usually not. The earpiece does not feed back into the microphone, so you get your half and little else. It varies by handset, so if it matters, test it once with a colleague before doing it on a real call.

Should I record on both at once as a backup?

You can, and you will get two calls in Junior rather than one better one. If you want a safety net for an important interview, the laptop recording is the one to trust, and it already keeps recording locally through a network drop.

Does a phone recording sound worse?

Not inherently, but placement matters far more than on a laptop. A phone in the middle of a table with four people around it will lose whoever is furthest away. Put it closer to whoever you most need to hear, and off any surface that carries vibration.

What if I only have my phone and the call is on Teams?

Join on the phone, put it on speaker, and record, accepting that the other side will be quieter and less accurate. It is much better than not recording. Say so in the call's details so whoever reads the transcript knows why it is uneven.