The CSE-800 has two HDMI™ inputs. Each of the HDMI input connectors are compliant to the HDMI 1.4b and 2.0r standard and are able of receiving a full 4k DCI (4096x2160) at 60Hz. Unfortunately, the current ClickShare product line does not support HDCP (neither 1.4 or 2.0), see Is ClickShare compliant with HDCP (High-Bandwidth Digital Content Protection)?.

The input board is capable of processing 60fps on a maximal resolution of 4K DCI (4096x2160). This processing capacity is shared over the two input channels. 

In case only one of the input connections is used, the input board is able to process the full input bandwidth of the input signal, meaning up to 4K at 60Hz and 60fps.

Whenever a second input is applied, the resources on the input board need to be divided proportionally over the two input signals. Each of the inputs will accept a 4K 60Hz stream but will drop to 30fps, meaning half of the frames will be dropped for each of the inputs. Two full HD input streams, each sharing at 60 fps, will not result in frames being dropped.

The difference between Hertz (Hz) and Frames per Second (fps) - The input connector specification is related to the bandwidth of the input electronics and is typically expressed in resolution and Hertz (Hz), whereas the processing capability indicates how much image data can be received and processed. This capacity is typically expressed in resolution and frames per second (fps).