What’s the difference between online machine learning and software that updates the model automatically and reestimates when new data are entered? Is online machine learning basically a software that updates the model automatically every time the data changes? So instead of having to run the same line of code again by a person and again by manually clicking  or edit the model as data comes in, it just model selects and recalculated the coefficients automatically? 
 A: I am not sure what you exactly call "online machine learning", but anyway we can think in two situations when a new data comes. For instance, suppose that your objective is to calculate the average of a set of points.
Before the arriving of the new point, suppose that the average is $\overline x$:
1) One possibility is to evaluate the average in the usual way: $\sum_{i=1}^{N+1}\frac{x_i}{N+1}$
2) Another possibility is to calculate the $\overline x= \frac{1}{N+1}x_{N+1} + \frac{N}{N+1} \overline x$.
I would call the second case "online learning", since you only update the last point. Note that in both cases the average is the same.
In general, all models that are a gradient based method (the parameters are evaluated using the gradient method) may estimated using online learning.
A: Online machine learning updates the estimates without re-running the full model. So it is not about having automatised the procedure, but about updating the estimate only based on the previous estimate and the new data (as in the example provided by DanielTheRocketMan). Re-evaluating the whole caboodle would be computationally expensive in the case of online sales and alike, and also not a good idea for estimates of drifting statistics (e.g. where the underlying model actually changes, as in the case of stock markets or climate change).
The classical approach is to use the current estimate as prior and the new data as observation in the Bayesian equation. That is typically not an option in "deep" learning, where the link above lists alternative approaches. 
