Your first one goes by a few different names. Haworthia Savannah aka x Gasteraloe Kabela. I believe it to be a Gasteraloe. They are prone to black spot. I have several;
The other most would say Haworthia limifolia but it looks more like the hybrid I got that is Tulista Pumila X Fasciata hybrid. Having Tulista it is larger growing then the Haworthia. Big difference is the inner pattern is broken up while limifolia is stright across like a washboard which is also it's nick name.
