吗 and 吧 at the end of a question I heard that ba (吧) can be used at the end of a sentence just like ma (吗). Per my understanding, it's not interchangeable with ma (吗) but a more playful way of asking the same question. (Some girl said I should use 吧 when asking her if she wants to go to lunch, idk what that means.)

So, when do you use each of these words? What are the connotations of each?
Firstly, you are correct... both can be used at the end of a sentence, but they do not have the same meanings.

吗 ma = question particle 

吧 ba = suggestive particle

Here's some examples:

你还好吗？(Nǐ hái hǎo ma) Are you okay? 

你还好吧。(Nǐ hái hǎo ba) Come on, you're okay, right? (suggesting that they're okay)


Or, In many cases 吧 is in response to 吗:

Person A: 好吗？Okay?
Person B: 好吧。 Fine...


That girl said you should use ba because she thought you should be more suggestive 

我们一起吃饭吧！（Wǒmen yīqǐ chīfàn ba）sounds more assertive than 你想跟我一起吃饭吗？（Nǐ xiǎng gēn wǒ yīqǐ chīfàn ma?）