What makes progressive verbs different from atelic, and can a verb be both atelic/telic, and/or progressive?

Verbs can be expressed in a progressive form if they have duration (ex: I was running. Running is something one does for an amount of time).

Telic verbs involve a change of state on completion, or have some intrinsic limit.

These are somewhat independent. Some examples:

An event that has duration and is atelic is sometimes called an activity. "I was running. " (note that "I ran" doesn't sound right unless context implies some intrinsic limit- for instance if you were talking about yesterday, or how you got to the park).

An event that has duration and is telic is called an accomplishment. "I was running to the store. I ran to the store." (Ok, telicity isn't really a property of verbs but of predicates. [run] is atelic, [run,to:store] is telic.

An event that does not have duration but is telic is called an achievement. "I found my keys." (one couldn't say "I am finding my keys" because finding something doesn't have duration)

Note that a sequence of same achievements can happen. This sequence has a duration, though the individual achievements do not. "I was finding good stories in the newspaper." Finding something is telic without duration, but finding a class of things has duration and is atelic. I think these later actions are called semelfactives.

This description of an underlying action (does it have duration? does its completion involve a change of state?) is referred to as aktionsart or lexical aspect. (lexical because it refers to the underlying verb and not its conjugation- though we saw that one must consider the verb's complements to characterize its aktionsart). Grammatical aspect is how the lexical aspect is present- [run,to:store] may have duration, but the lexical aspect of "I ran to the store" places the listener after the action as is independent of whether the action has duration. "I was running to the store" places the listener in the middle of the action, implying it has duration. These two phrases have different grammatical aspect while working with the same lexical aspect.