Quick answer
"On the other hand" is a phrase which is often translated as "por otro lado", and "anyway" is an adverb which is often translated as "de todos modos". Learn more about the difference between "on the other hand" and "anyway" below.
on the other hand(
A phrase is a group of words commonly used together (e.g once upon a time).
1. (indicating opposition)
a. por otro lado
On the one hand, I love shopping, but on the other hand, I need to save for college.Por un lado, me encanta ir de compras, pero por otro lado, tengo que ahorrar para la universidad.
b. por otra parte
On the one hand, I promised I'd buy her lunch, but on the other hand, she still owes me dinner.Por una parte, le prometí que le compraría el almuerzo, pero por otra parte, aún me debe una cena.
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An adverb is a word that describes a verb, an adjective, or other adverbs (e.g. to run quickly, very tired).
1. (in any case)
a. de todos modos
It's probably raining there anyway.Probablemente está lloviendo allí de todos modos.
b. de todas formas
I don't know what he's talking about anyway.De todas formas, no sé de qué habla.
c. de todas maneras
Despite the risk, some people continue to smoke anyway.A pesar del riesgo, algunas personas siguen fumando de todas maneras.
2. (at any rate)
a. bueno
Anyway, what were you saying before I interrupted you?Bueno, ¿qué decías antes de interrumpirte?
b. bien
Anyway, let's go.Bien, vámonos.
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