TE is a less severe type of hair loss brought about by stress, and it's one of the more common types as well.
According to Healthline, "[It] occurs when there’s a change to the number of hair follicles that are actually growing hair. If this change occurs during the telogen — or resting—phase of hair growth, it can result in shedding."
The good news is that with TE you probably won't lose all of your scalp hair and your hair will likely grow back.
Healthline explains, "The hair loss that occurs from TE is fully reversible. TE doesn’t permanently damage the hair follicles. The cause of your TE will affect whether your hair grows back in a few short months, or longer."
AA on the other hand is a more severe condition and an autoimmune disease.
Healthline summarizes, "It develops when your immune system attacks your hair follicles. This may be triggered by stress, and it can result in hair loss."
With AA, your hair might grow back and fall out again in cycles. Without any cure for AA, this is a much more difficult condition to death with although there are some prescriptions available.
Both TE and AA can occur as the result of stress, but what happens to your hair (and the longterm effect on your hair health) is unique in each case.
With that in mind, it's important to work on ways to manage your stress before it becomes a serious problem for your health.