This is a very good question, because the words appear to have identical spelling/appearance.
The two Hebrew words are understood to express a subtly different concept based on their context. The interlinear grammatical notes give the following bits of information.
Proverbs 8:4 has אֶקְרָ֑א, which is a Qal imperfect verb in first-person common singular.
Psalm 55:16 has אֶקְרָ֑א, which is a Qal cohortative imperfect verb in first-person common singular, based on context.
Essentially, it boils down to this: The Hebrew mindset allowed the use of ordinary references to God, even commands/telling God what to do, with the caveat that people always understood that since one cannot actually tell God what to do, the verb in that context implied a degree of wishful thinking or desire rather than actually representing such a bold assertion. This can be expressed in English variously with a modal verb (such as "will" in this case, or "shall", "may", "might", etc.) or some form of a subjunctive tense.
A Qal imperfect, also called Yiqtol, can actually be past, present, or future, but because it implies a continuing, incomplete action, it is often translated as a future tense verb. It bears some resemblance to an English present participle ("-ing" verb), except that it is not merely a participle, but a verb that stands on its own.
This explains why the "I will call..." is a typical translation for this verb form.
In Proverbs 4:8, the object of the verb, instead of being God, is people--and this allows for a more blunt or literal translation: "I call...." It should be understood that in either case, this imperfect verb implies an ongoing action, and not merely one that will complete in a single instance, nor that is already complete.
The essential difference between the two Hebrew words and their translations in these two verses is simply that one is applied toward God, while the other is applied toward man. The Hebrew mindset automatically understood that when addressing God one was not to speak cavalierly, and while the actual words might be identical, the meaning was understood to be less assertive and more respectful. This is yet another example for why, in Hebrew, context is of paramount importance.