They're not color spaces themselves. They are just mappings of the RGB colorspace. They are not identical.
In HSV, [1 0 0] and [1 1 1] are both 100% value, whereas in HSI, red is 33% intensity; in HSL, it's 50% lightness.
HSV and HSL are fully constrained, meaning no value of H, S, or V/L within the normal ranges can select a color which is outside the standard data range for RGB. The top half of HSI is not constrained. Significantly increasing I for colors near the R=1,G=1, or B=1 faces of the RGB cube will push those color points outside the data range.
HSL has a symmetrical saturation space, unlike HSV or HSI, which tends to lend it to less garish results when doing hue adjustments or HS swaps between images.
Does any of that have bearing on how they are or should be used and specified for tasks in Matlab? I don't know. I'm just saying they're not the same. I'll leave it fellow time-travelers to look up the relevant wiki articles to address any surviving curiosity.