What is the difference between a "time series" and a (discrete-time) stochastic process?
A time series is a sequence of actual, fixed, values, like:
61, 63, 58, 64, 56, 48, 39, 42, ...
A stochastic process is a sequence of random variables that have some kind of specified correlation or other distributional relationship between them. Stochastic processes are often used in modeling time series data- we assume that the time series we have was produced by a stochastic process, find the parameters of a stochastic process that would be likely to produce that time series, and then use that stochastic process as a model in predicting future values of the time series.
Basically, a stochastic process is to a time series what a random variable is to a number.
The realization (the "result", the observed value) of a random variable (say, a dice roll) is a number - (but, as it's a random variable, we know that the number can take values from a given set according to some probability law).
The same applies to stochastic process, but now the realization instead of being a single number is a sequence (if the process is discrete) or a function (if it's continuous). Basically, a time series.