Of the two you list, it is probably the anemones - freesias have little corms that are somewhat pear-shaped, narrow the top, wide at the bottom. Anemone coronaria are kind of triangular; Anemone blanda (and nemerosa) do produce extensions. Ranunculus also produce gnarly corms, with finger-like (or banana-like) extensions - even more so than the anemones.

Here is a link that might be useful: anemones and ranunculus corms - ignore planting times, NZ site

ranunculus came to mind when you said bananas.