A regularly clocked sample and hold discretizes a signal in time, but retains the continuous voltage.
The other way around is not possible since quantized values are inherently discrete.
I see some disagreement about a signal quantized to a set of levels being inherently discrete in time.
Let's consider what such a quantized but continuous time signal would have to look like. Quantized means that the signal level is expressed as a number at any one instance in time. To not be quantized in time, this number must reflect every change of the input value crossing between quantization domains. This is simply not possible as it requires infinite bandwidth.
Consider the simplest quantization scheme of all, which is a 1 bit A/D, also known as a comparator. The input signal is quantized to only one of two states. To be continuous in time, the comparator would have to respond to every possible excursion of the input signal accross the boundary between the two quantization domains. However, any real comparator will some length of excursion that it will not reflect on its output. The comparator will be "blind" to the input signal crossing the threshold for some minimum time after it responds to a change. Put another way, to not discretize the input would require infinite bandwidth, which is not physically realizable.