Different tires can have different handling responses, but also different actual sizes even though they have the same size label on the sidewall.

First difference can be with rolling diameters. They need to be very close side to side. If not, you are wearing the differential, and risking intervention by the traction control system which sees a different speed left and right.

Second difference is with handling characteristics. This is entirely mechanical, not electrical. Different tires respond differently, and you can get unpredictable (and thus unsafe) responses from having different tires left and right.

Third difference is with the electronic systems that monitor vehicle dynamics. This is the electrical intervention side of the second point. The vehicle sensors measure yaw, steering angle, etc, and respond by applying a single brake or reducing power. If the responses are 'out of range' ie not what the computer expects, which is more possible with different tire handling characteristics, you can get electronic interventions that you don't want.

Short answer is you should have the same tires on a single axle, with similar wear %. That extends to all four tires, but not to the same extent. The rolling diameter is important for all four, but the tread pattern not so critical front/rear. I would still strive to have all the same tires on the vehicle, with similar wear %.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue