Difference between O-QPSK with half-sine shaping and MSK?
OQPSK in it basic form uses square pulses. However we never transmit an unfiltered signal like that, at least not these days, due to spectrum spreading. HSS shaping reduces the spread significantly.
MSK and shaped OQPSK are essentially the same waveform. They can be demodulated by the same receiver. That receiver can be finite or zero IF. Assuming the transmitter is coherent, the receiver can benefit from coherent demodulation with an improvement in sensitivity, or incoherent with a benefit in cost.
There is a lot of money to be made in the business of communications, so there's a lot of fighting over intellectual property around the modulation schemes that can be used to lock out other companies and extract license revenues. Many companies therefore seem to obfuscate and confuse when describing how their systems work. When working a couple of decades ago, I had to defend our products from a vexatious suit from a company claiming a patent on, as it happens, OQPSK. Fortunately I managed to find prior art in a very old published text book, which saw them off.