There is no difference in meaning. Both are correct and natural (except for a tiny detail which I'll mention later). A native speaker would probably choose unconsciously, based on what had gone before, what they wanted to emphasize, and what they were planning to say next. For example, if you asked me "Who did you speak to?" I would be likely to use #2. If I had just said "...so then I called them," I would be more likely to use #1. Here's the tiny detail. It has nothing to do with your question. People who are trying to use strictly correct English would phrase #1 as "The lady to whom I spoke on the phone..." The theory is that "who" is a subject pronoun, "whom" is an object pronoun, and is the object of "spoke to." The problem is that nowadays, the "correct" form is rarely used--even by "educated" speakers. Merriam-Webster says, unhelpfully: "Trust your instincts... actual usage doesn’t always follow the strict rules of grammar. Our ears are our guides, and there are many constructions (like "Whom did you speak to?" vs. "Who did you speak to?") in which 'whom' may be technically correct but still feel fussy or unnatural. In these cases, it is perfectly standard to use 'who.'" Your #1 sounds natural. "The lady to whom I spoke on the phone" sounds unnatural.

#1 contains an error: grammar requires that you use the accusative (objective) pronoun "whom", not "who" because it is the object of the preposition "to". There are people who will tell you that bad grammar is not important. IGNORE THEM! Do it right not simply to be obedient, but because it will cause you to think about the logic of your sentences. Using "whom" as needed will help you to think logically and will increase your fluency. The sentences have entirely different structures. Also #2, though correct, is poorly designed because the word order is confusing. Let's analyze each one: #1 SUBJECT = "the lady" VERB = "told" INDIRECT DIRECT OBJECT = "(to) me" The adjective phrase "to whom I spoke" modifies "lady" (clearer if "to" is placed next to "whom") DIRECT OBJECT and NOUN PHRASE = "to call back later". The adverb phrase "on the phone" modifies "spoke" #2 SUBJECT = "I" VERB = "spoke" INDIRECT DIRECT OBJECT = "(to) a lady" The adverb phrase "on the phone" modifies "spoke" The adjective phrase "who told me to call back later" modifies "lady". #2 is poorly designed because phrases are far from the words they modify. "On the phone" works better if placed close to "spoke". "Who told me" works better if placed next to "lady", like this: "I spoke on the phone to a lady who told me to call back later."