I suppose that just in different tutorials the same metric is indicated with different names. You can use any of these results. You also can compare if they have the same values (if rarefied table is the same).
Core-metrics is a pipeline, which computes a lot of metrics at the same time. Qiime diversity alpha plugine computes only the metric you choose. It should be the only difference, if you are using the same rarefied table.
You mean, as long as I used the same rarefied_table, even if I used different way (‘qiime diversity alpha’ or ‘qiime diversity core-metrics-phylogenetic’, they’re going to be the same result, right?
Hard to tell. For me the most convenient way was to take four alpha diversity metrics produced by core-metrics plugin, plot them in one plot for my samples and look into the differences between them, which metrics are more influenced by factors in my metadata file, and which are not. And based on it I am drawing some conclusions. But I can’t say that one metric is better or worse. Take a look on all, choose the metrics that better correspond to your data, try to figure out, why is it so.