There seems to be some confusion again with common names - Aloe vera is Aloe vera :-) Although that term is sometimes used to refer to ANY kind of aloe, there are not two species of true or common, aka medicinal aloe. There ARE many species of aloe....as many as 400 have been registered but true aloe, Aloe vera (formerly Aloe barbadensis), is the one noted for medicinal purposes. There is some documentation that Aloe arborescens also has similar medicinal properties but as the species name suggests, this has a much more tree-like growth habit and develops a distinct stem or trunk. The difference in growth habits between the two plants shown in the pics is simply due to age and maturity. Aloe vera will form a full rosette if given sufficient time and proper growing conditions. Check the Wiki photo linked below. The smaller ones that appear to only grow laterally rather than in a round rosette of leaves are just young, immature plants (offsets or pups) and hampered from full development by lack of time and indoor growing conditions. Here is a link that might be useful:

First, the plant is Aloe variegata Second, remove it from the pot. Those two plants have different cultural requirements, and will do better in their own pots. Third, carefully remove the pups from the mother aloe. You may find more that you can't see now. They grow on specialized 'roots' called rhizomes. If these can't find a way to the surface, they wind around the pot, sometimes emerging from the drain hole. You will need sharp shears or scissors. Cut the pups about 2 inches below the lowest leaf. Let them dry in the air for a few days, allowing the cut end to callous. Then plant in dry soil, and wait for roots to form. Aloe variegata is a 'winter grower' meaning Sept-Nov, and Feb-April. It is summer dormant, giving too much water at that time will promote root rot. Depending on where you live, it should be entering a period of slow growth until early spring. Don't give lots of water during the coldest and darkest months. Fourth, now that you have removed all the soil, rhizomes, and pups, you can carefully examine the main stem for signs of fungal infection. If everything looks OK, repot in a six to 8 inch diameter container. You can bury it a little deeper if you like to prevent it from leaning over. Soil should be at least 75% percent or more inorganic materials like pumice (scoria), perlite, gravel, turface, etc. with particle sizes in the 1/8 to 3/8 inch range. Use no sand in the mix. Most commercial C&S mixes contain too much peat. A very quick draining mix is required. Lastly, your recent rapid growth may have been caused by low-light etiolation. This is when the stem grows quickly and the space between leaf nodes gets larger as the plant stretches for more light. Give this plant as much sunlight as possible. This is the time of year when you would expect growth. More light will produce a shorter, more compact, and tougher plant. I'm sure you will have lots of other questions which the people here will be glad to answer. There is a link to more info on this plant at the bottom of my post. Happy Growing! Brad Here is a link that might be useful: Aloe variegata

Aloe vera leaves might grow more horizontal if in lower light conditions. In higher light conditions they typically have a more closed rosette. Also, if under watered a bit their leaves can curl and look canoe-like. I think the curling you're thinking of and reading about online are two different things. A picture of your plant would better help us sort out whats going on.

Sarah I never grew Aloe vera, but have few aloes. Look at this thread: -beheading plants - showing different aloe being beheaded, and I think that same could work for your plant. There are many other/different succulents shown in same thread. I am posting this also to bring your thread up, so someone with A. vera experience may see it and respond.