I love the Shebeest Board shorts; but I bought my first pair in brown and they were comfortable, a bit big. The next year, I bought black ones and they are tight, in the same size! I've had them for 5-6 years.
The "liners" are shorts that come under the board shorts, baggies, various knickers. Sometimes they are attached with loops, but you can cut them off. The actual shorts part is not as compressive as regular shorts.
You can also buys liners separately. I have a great pair from Sugoi. The shorts part is mesh, but the chamois is like other Sugoi shorts. I've ridden 50 miles wearing them.
You can also buy underwear with a thin chamois here on TE. Unfortunately, the smallest size was like a diaper on me, so I ditched them. But DH wears his for casual rides, under his regular clothes.