Will a signal booster work for both phone calls and data (internet)?

Yes, a signal booster will work for both phone calls and data.

All modern signal boosters use a five-band amplifier, but you may come across some legacy dual-band amplifiers while searching for a booster solution. We'll cover both. 

Five Band Signal Boosters

Five band signal boosters will boost voice calls, 3G, 4G HSPA+, 4G LTE and 5G (as long as it's deployed on one of the five frequency bands) so you'll have better voice calls and faster data for any network that you're on. You should almost always use a five-band amplifier for boosting signal.

Dual Band Signal Boosters

Dual-band signal boosters only boost two of the five available frequency bands, so if your carrier is using one of the bands that is not boosted by your amplifier, then you will not receive any benefit. We highly recommend using a five-band booster over a dual-band system.