I must admit I ask my students a question that is very similar to this one, though I think I might adopt the wording of this question in future! The key theme of marriage, and in particular the different ways in which female characters find husbands for themselves is of great importance in this wonderful novel. Clearly, what is interesting about both Charlotte and Lizzie is that both take financial considerations into account. However, the crucial difference between them is that Lizzie also takes character into account, which is something that her erstwhile friend Charlotte Lucas fails to do. Note what she says to Lizzie in Chapter 22 to justify her decision to marry the ridiculous Mr. Collins:
I am not romantic, you know. I never was. I ask only a comfortable home; and considering Mr. Collins's character, connections, and situation in life, I am convinced that my chance of happiness with him is as fair as most people can boast on entering the marriage state.
For Charlotte, at her age and station in life, we must understand that marriage is an escape from becoming an old spinster left to look after her mother. This is something that the recent film version of this book starring Keria Knightley made explicit. Love for her is not important. Marriage is nothing more than a means of gaining independence and financial security.
Let us consider Lizzie briefly for one moment. We cannot say that she is exactly the same as Charlotte. After all, if this were the case, she would not have refused Darcy the first time he proposed. This clearly indicates that to Lizzie how she feels about the other person is very important. She has to love them and feel that there is a respect and equality of character that will make a marriage happy. However, at the same time, as she shows in her relations with Wickham before she realises the truth about him, she recognises that any partner, whether she loves them or not, has to occupy a certain social standing and wealth. It is rather ironic that the scene that initiates the change in Lizzie's affections towards Darcy is when she sees him at Pemberley, with all of his wealth on display. Therefore we can't entirely say that Lizzie and Charlotte are identical. Wealth and social standing are important to Lizzie, but they need to be accompanied with love, which is something that was absent from Charlotte's rather mercenary attitude to marriage.