Pineberry is a strawberry.
This is why botanical (latin) names are so useful.
The pineberry is the same Fragaria × ananassa as all other “garden strawberry’s”
It originated from a cross between Fragaria virginiana and Fragaria chiloensis (the chiloensis giving both light red and white fruits)
This means it can easily be pollinated by other garden strawberry’s, because it is one itself.
Both parent species and Fragaria Ă— ananassa are octoploid. (8 x 7)
Judging from your pictures, you have the Fragaria Ă— ananassa pineberry. And not a wild with strawberry like Fragaria nilgerrensis (diploid 2 x 7)
I have both. And nilgerrensis has quite a different leaf. And is much smaller.
The “pinebeery” cultivar of strawberry for me, makes a lot of runners and huge leaves. (if had 70+ runners of a 2y old plant)
Similar but more than the Fragaria Ă— ananassa frau mieze schindler
Although that one, unlike most Fragaria Ă— ananassa cannot self pollinate.
With bubblegum strawberry i assume you mean. A Fragaria moschata (6 x 7) Sometimes marketed as bubblegum strawberry. But it’s a musk strawberry. (also called large forest strawberry where i live)
It does not readily cros with Fragaria Ă— ananassa. And most cultivars of Fragaria moschata need a pollinator. (most Fragaria moschata are either male or female. Although some self pollinating cultivars exist)
I have a Fragaria moschata. And again it’s leaves are quite different from Fragaria × ananassa
The flowers and berries are also on quite a high stalk. Above the leaves. Where Fragaria × ananassa usually “hides” the flowers and fruits below the leaves.
I don’t have a pink panda. But i think that one is also octoploid. So that’s the most likely one to cross with the “pineberry”
Most strawberry’s (if any) don’t spread by rhizome. They spread by runners. (Some alpine strawberry = Fragaria vesca don’t make runners. And i have split large plants of these. But mostly these are propagated by seed)
“pineberry’s” do make more runners than most other Fragaria × ananassa cultivars. This i think in part is, because they make less fruit. And thus have more energy to put into runners. You see quite the opposite in some everbearing Fragaria × ananassa cultivars. Those tend to overproduce on fruit and make almost no runners. (although if you remove flowers/fruit suddenly they make runners)