What approximate resolution did Beta SP correspond to?
The resolution is correct, but your understanding of how that is measured is confused.
Analog video consisted of a series of continuous horizontal lines. Don't confuse the number of vertical lines with &quot;lines&quot; of horizontal resolution. When you talk about horizontal lines you're actually talking about how many line pairs—or literally how many vertical black and white lines—the format could reproduce. To compare it to pixels, consider that it takes two pixels to reproduce a line pair: one black pixel and one white pixel. So double the analogue measurement to get the digital comparison.
So while line pairs is the measurement used for the horizontal resolution, the vertical resolution is locked to the television standard, 576 lines for pal, and 480 lines for NTSC.
The horizontal resolution can be calculated from the bandwidth using the rule of thumb for resolution of 80 lines per MHz of luminance* bandwidth. Betacam had a bandwidth of 4.0-4.5 MHz, which works out at 320-360 lines. This equates to 640-720 pixels of resolution, or roughly the same as DV.
TL;DR: Betacam's resolution was roughly equivalent to 720x576 for PAL, 720x480 for NTSC
*luminance had higher bandwidth than chroma, just as digital formats subsample the chroma information, usually at half or even quarter resolution.