The Nvidia GeForce RTX 3060 Max-Q (for laptops, GN20-E3, Max-Q) is the former name for a RTX 3060 Laptop GPU with Max-Q technologies. In previous generations, the Max-Q name was used for low power versions. With the RTX 3000 series, every TGP-version can now use Max-Q technologies and all GPUs are called RTX 3060 Laptop GPU (60 - 115W).
The Nvidia GeForce RTX 3080 Max-Q (for laptops, GN20-E7 Max-Q) is the former name for a RTX 3080 Laptop GPU with Max-Q technologies. In previous generations, the Max-Q name was used for low power versions. With the RTX 3000 series, every TGP-version can now use Max-Q technologies and all GPUs are called RTX 3080 Laptop GPU (80 - 150W+).
The Nvidia GeForce RTX 3060 Mobile (for laptops, GN20-E3, Max-P) is the third Ampere graphics card for notebooks in early 2021. It is based on the GA106 Ampere chip and offers 6 GB GDDR6 graphics memory with a 192 Bit memory bus. It supports PCIe 4.0 and will be available in different variants from 60 or 115 Watt (TGP). As package the notebook graphic card uses GB5-256 and the chip size is 40x40mm. The GPU supports eDP 1.4b to connect the internal monitor.
There is no more Max-Q variant (formerly used for the low power variants) but every OEM can choose to implement Max-Q technologies (Dynamic Boost, Whisper Mode).
The performance depends on the TGP setting and cooling of the laptop. On average it should be similar to the older GeForce RTX 2070 Super Mobile and therefore best suited for QHD gaming (very demanding games). Less demanding games like Star Wars Squadrons should be playable in 4k with maximum detail settings. The similar named RTX 3060 desktop card is significantly faster.
The GA106 chip offers 3,840 FP32 ALUs of which half can also execute INT32 instructions (i.e. 1,920 INT32 ALUs). The mobile RTX 3060 uses all 3,840 cores on the chip. With Turing all shaders could still execute FP32 or INT32 instructions. The raytracing and tensor cores on the chip were also improved according to Nvidia. The Ampere chips also include an improved 5th generation video encoder (NVENC for H.264 and H.265) and a 7th generation decoder (for various formats now including AV1).
The GA106 chip is manufactured by Samsung in 8nm (8N), which is not quite able to keep up with the 7nm node at TSMC (e.g. used by AMD and also for the professional GA100 Ampere chip).