In hardware, pulse measurement and semi-period are the same measurement. Both measure the high and low times of a pulse. The functional difference between the two measurements is how the data is returned. In a semi-period measurement, each high or low time is considered one point of data and returned in units of seconds or ticks. In a pulse measurement, each pair of high and low times is considered one point of data and returned as a paired sample in units of frequency and duty cycle, high and low time or high and low ticks. When reading data, 10 points in a semi-period measurement will get an array of five high times and five low times. When you read 10 points in a pulse measurement, you get an array of 10 pairs of high and low times.
Also, pulse measurements support sample clock timing while semi-period measurements do not.