Yes, the verbal components on the two tests, in their current formats, are different. SC stands for two different things on the GRE (sentence completion) and the GMAT (sentence correction).
The GRE has four types of questions on its verbal reasoning section, which currently gives you 30 questions in 30 minutes:
1. Sentence Completion (or Text Completion) - You're given a sentence with one or more words removed and replaced with blanks. You must select the word or words that best fit the blanks. Like Madlibs with grad-level language.
2. Analogies - You're given a pair of words that have an identifiable and specific relationship, as well as a prompt word. You then choose a fourth word that will have the same relationship to the prompt word as seen in the example pair. SAT on steroids.
3. Antonyms - You're given a prompt word and you must find its opposite amongst the answer choices. Unless you're incredibly wildly read, it's nearly certain you will encounter some words (at the very least while preparing for the exam) that you have never see in print or heard spoken.
4. Reading Comprehension - You read a passage and respond to both big-picture and specific-detail questions.
On your exam, you'll receive these question types in roughly equal proportions.
The GMAT, like you know, has three types of questions on its verbal ability section, which gives you 41 questions in 75 minutes:
1. Sentence Correction - You get an example sentence or passage with an underlined portion and you determine if the underlined portion is "grammatically correct."
2. Critical Reasoning - You get a passage and answer questions about the logic internal to or implied by the text.
3. Reading Comprehension - For all intents and purposes, this section is the same (the only verbal question that is the same on the two current tests).
On your exam, you'll receive these question types in roughly equal proportions.
The new GRE in 2011 will alter the verbal reasoning section in several ways. Antonyms and Analogies will be replaced with a new question type called Sentence Equivalence, which will be similar to the current Sentence Completion, except you're going to select multiple usable answer choices. Sentence Completion is going to be renamed Text Completion and become somewhat more involved. Reading Comprehension should remain more or less the same.
AFAIK the new GMAT will not dramatically change the current verbal section.
With the GRE and GMAT verbal exams so different (except for the reading comprehension section) you'll need to prep differently and you should decide whether you really want to take the GRE before starting.