What's the difference between 食べていよう and 食べましょう?


From a glance I'm guessing て + いる (~ていよう) is the volitional casual and ~ましょう
is the polite form of it?

Are these the same meaning? "Let's eat" or am I making a wrong assumption?




> 「食{た}べましょう。」
>
> 「食べていよう。」

There is such a huge difference in meaning between those two expressions that
they would rarely, if ever, be interchangeable.

「食べましょう。」 is the default " _ **Let's eat!**_ " or " _ **Lets's dig in!**_ ".
You just start eating after having said it.

「食べていよう。」 means " _ **Let's continue/keep eating!**_ " and it can only be said
in certain (special) situations.

An example situation:

Something happens just when a group of people are starting to eat, one of them
must leave the table to check something someplace. It could be a phone call or
a knock on the door; It could be anything that could possibly interrupt the
meal for a while. The rest of you have a choice between continuing to eat and
stopping eating to wait for that one person to return. If you decide to
continue eating, you can say 「食べていよう」.

Thus, 「食べましょう。」 would be used far more often than 「食べていよう。」. No comparison
here, really.




> 「食{た}べましょう。」
>
> 「食べていよう。」

There is such a huge difference in meaning between those two expressions that
they would rarely, if ever, be interchangeable.

「食べましょう。」 is the default " _ **Let's eat!**_ " or " _ **Lets's dig in!**_ ".
You just start eating after having said it.

「食べていよう。」 means " _ **Let's continue/keep eating!**_ " and it can only be said
in certain (special) situations.

An example situation:

Something happens just when a group of people are starting to eat, one of them
must leave the table to check something someplace. It could be a phone call or
a knock on the door; It could be anything that could possibly interrupt the
meal for a while. The rest of you have a choice between continuing to eat and
stopping eating to wait for that one person to return. If you decide to
continue eating, you can say 「食べていよう」.

Thus, 「食べましょう。」 would be used far more often than 「食べていよう。」. No comparison
here, really.

