Up sampling is when you increase the sample rate of a continuous signal. Modulation is when you, by multiplying with a carrier, shift the base frequency of a signal. But what is up conversion? How is it related with the above mentioned terms?
Your first sentence is not correct. The terminology of 'sample rate conversion' operations is often misused. I suggest you replace your first sentence with, "Interpolation is when you increase the sample rate of a DISCRETE signal sequence." I'd also replace your second sentence with, "Modulation is when you, by multiplying with a carrier frequency, shift a signal's spectral components up in frequency by a fixed amount." (The term "modulation" is typically used when talking about continuous signals.) As far as I understand the terminology, "up-conversion" is when you shift the spectral components of a discrete sequence up in frequency by a fixed amount. [-Rick Lyons-]