Recording drums is a fascinating art.
As advised, a lot of drummers are hidden behind sound screens, which can be solid because no-one needs to see the drummer.
On stage, if it s a smaller stage especially, the drum sound can ‘leak’ into other microphones which makes a clean sound mix difficult. That matters less in jazz than in rock, hence why jazz bands don’t usually bother.
In some cases, the sound leakage is the desired effect. When Led Zeppelin recorded tracks like When The Levee Breaks, they used Hedley Grange studios, and John Bonham’s drums were set up in the hall, with ambient mics on the upper floors and staircase. The already massive sound of his 24” bass drum, and power with which he kicked it, was enhanced by the natural booming echo of the old building which gave birth to a classic, and much sampled drum sound.
That’s the drum sound you can hear on The Beastie Boys’ Fight For Your Right To Party, and many more.