I'm analyzing the results of an educational research study wherein learners had the opportunity to conduct multiple attempts (trials) at a task. The scoring mechanisms are the same for each trial. Originally we were just interested in taking their "best" scores, but looking at the data, we can see that some learners have very different trajectories (in terms of the trial-to-trial change in the scores) than others, and visual inspection suggests that it may be the case that these trajectories are more similar to each other within the different conditions than across them (we have 3 conditions).

I have a good grounding in basic, single-measure statistics, but I don't know what search terms I should use to find methods that compare measurements-over-time to other measurements-over-time. The information I have found on time-series analysis seems to suggest that I should be aggregating the scores at each time step - but this would be inappropriate, as (a) I am not interested in the exact score at each trial, just the way that score changes from trial-to-trial, and (b) aggregation would lose the information about how each learner changed his or her score.

So I assume that I first want to compute the "lag" between each score for each learner, but now I'm stuck on what to do next - I'm not interested in forecasting or detecting cyclic trends (which is what most time series analysis seems concerned with), I just want to be able to (1) say whether the patterns in lag within each of the conditions are statistically more similar to each other than the patterns across the three conditions, and (2) definitively characterize the lag patterns themselves (e.g., in terms of monotonicity and/or slope if the lag values were plotted over time). I feel like there must be an approach out there for this, I just haven't found the right search terms to describe my problem space or the right test names to look for. Any advice or links to references would be appreciated!