"Upsampling" is the process of inserting zero-valued samples between original samples to increase the sampling rate. (This is called "zero-stuffing".) Upsampling adds to the original signal undesired spectral images which are centered on multiples of the original sampling rate.
o·ver·sam·pling
/??v?r?sampliNG/
noun
Electronics
noun: oversampling; noun: over-sampling
the technique of increasing the apparent sampling frequency of a digital signal by repeating each digit a number of times, in order to facilitate the subsequent filtering of unwanted noise.
Two different thinks - oversampling is related to converting analog signals to digital at higher sampling rates than the target rate and then downsampling and upsampling is used to convert digital in digital at an higher sampling rate.
Just to add confusion - an oversampling DAC needs upsampling!
From a technical standpoint, these terms are largely synonymous. Both involve multi-rate (differing input to output sample rate) digital filtering techniques. It seems, although there is no rule about this, that for audio applications 'oversampling' is taken to be a power-of-two integer ratio (x2, x4, x8, x16, etc.) multiple synchronous technique, while 'upsampling' is an arbitrary ratio (x1.5, x3.15, x4, x5.7, etc.) multiple asynchronous technique. Oversampling is usally associated with the purpose of digital signal reconstruction, while upsampling is usually associated with digital signal asynchronous-sample-rate-conversion (ASRC). At their core, both typically utilize brickwall FIR filter engines.
A well known side benefit of ASRC is that it can enable very effective jitter suppression. Also, the fact that ASRC is often utilized in non-integer ratio rate conversion can produce distortion artifacts in certain situations, making ASRC controversial for use as a digital reconstruction filter. Some DACs utilize both ASRC followed by an oversampling digital reconstruction filter.