Why do laptop batteries have so many terminals?
Google "laptop battery pinout".

Typically you'll have:


Plus and Minus power terminals (maybe several contacts each for higher current)
Some form of communication like I2C
Temperature sensing (for example a thermistor)


Your typical laptop battery has several cells in series, so it requires balancing which is usually implemented in the battery management PCB inside the battery. This also handles protection for conditions like short, overcharge, overdischarge, etc. The laptop itself doesn't need to know the details about internal battery chemistry, that's the battery management PCB's job.

Also important is reporting state of charge accurately. This is difficult to do with voltage alone on Lithium battery, so you might find something like a coulomb counter, which implies values stored in a RAM which must be in the battery. The I2C bus also allows communicating useful information like battery capacity, maximum charge current for the charging circuit, or authentification for higher profit margins...

A cellphone runs on one cell, thus it does not require balancing or other complex functions. It will most likely just have plus, minus and temperature. If the battery is removable then it should have a protection, at least against shorts, in case the user  stores a battery along with metal objects like keys. If it is internal to the phone, then it probably won't have a protection PCB.