1. find differences or features that stand out
distinguish between, distinguishable features
When you distinguish something from something else you identify the features that make it unique or different from something else. You might say the 'distinguishing feature' of a robin is its red breast for example. This is the feature that identifies it from other birds. You might want to 'distinguish' what the problem is with something that is not working or 'distinguish' the factors or steps involved in something. This is a formal phrase used in academic and professional contexts more than social ones. Don't confuse this with the adjective 'distinguished' (see Meaning 2).
2. appear dignified or noble
he looked very distinguished in his new suit
This is a very different use of the word 'distinguished', and it is always in the past tense form. However, it is not a verb, and it is used to describe someone's appearance. It means that they look noble or sophisticated, and it usually refers to how someone is dressed.