Rav Yosef Dov Ber Soloveitchik mentions this topic in the essay פסוקי דזמרה in volume 2 of שעורים לזכר אבא מרי ז״ל (pages 36-38). He asks:
- Since we say that required prayer (תפילת חובה) corresponds to bringing the tamid offering (קרבן תמיד), and the latter must come from all Israel, how could it be that a minyan that does not include all of Israel bring such an offering?
- Even stronger than question 1: how could an individual bring a communal offering?
- How could it be that each minyan brings a tamid, when we only need one tamid for all Israel?
To put it simply, he explains that all the prayers of all minyanim and all obligatory prayers of individuals combine into one tamid for all of Israel. He contrasts this to a voluntary prayer (תפילת נדבה) of an individual, which is an individual offering (קרבן יחיד) "from beginning to end".
So to answer your question, according to Rav Soloveitchik, both communal prayers and individual obligatory prayers correspond to the tamid offering, whereas voluntary prayers of an individual correspond to individual offerings. See the essay itself for textual support for his assertion, and more nuance/details.