Alternately means switching between two alternatives, alternatively means doing something different.

I love pizza and Mexican food, I eat them alternately.

Means Monday I ate Pizza, Tuesday Tacos, Wednesday Pizza again, Thursday Buritto, Friday went to the Hospital to get my arteries roto-rooted.)

I love pizza but alternatively I eat Mexican.

Means both choices are good, but says nothing about when or the order in which I eat them.

Alternately is about switching. Alternatively is about enumerating options.

Alternately means switching between two alternatives, alternatively means doing something different.

I love pizza and Mexican food, I eat them alternately.

Means Monday I ate pizza, Tuesday tacos, Wednesday pizza again, Thursday burrito, Friday went to the Hospital to get my arteries roto-rooted.

I love pizza but alternatively I eat Mexican.

Means both choices are good, but says nothing about when or the order in which I eat them.

Alternately is about switching. Alternatively is about enumerating options.

Alternately means switching between two alternatives, alternatively means doing something different.

I love pizza and Mexican food, I eat them alternately. (Means Monday I ate Pizza, Tuesday Tacos, Wednesday Pizza again, Thursday Buritto, Friday went to the Hospital to get my arteries roto-rooted.)

I love pizza but alternatively I eat Mexican. Means both choices are good, but says nothing about when or the order in which I eat them.

Alternately is about switching. Alternatively is about enumerating options.

Alternately means switching between two alternatives, alternatively means doing something different.

I love pizza and Mexican food, I eat them alternately.

Means Monday I ate Pizza, Tuesday Tacos, Wednesday Pizza again, Thursday Buritto, Friday went to the Hospital to get my arteries roto-rooted.)

I love pizza but alternatively I eat Mexican.

Means both choices are good, but says nothing about when or the order in which I eat them.

Alternately is about switching. Alternatively is about enumerating options.