Not quite. The Browning safety is on the slide, not the frame like on the Beretta.Unkempt1 and all,
The Browning .380 BDA is a Beretta. The only difference being that the BDA has a solid slide, while the Beretta's remove the top of the slide, a la the 92F series.
For a short time Browning marketed the SIG as the Browing DA.a long time ago I saw a Sig 220 .45 that was marked Browning..if memory serves it had a heel clip magazine release