From my understanding it seems Munich is a base malt whereas Caramunich is a crystal malt, and the numbering is the amount of roasting.
Is that correct? Are Caramunich and Munich interchangeable?
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As the other answers have stated, the malts are indeed different. As with all malts, they can vary between malt companies but these varieties are different regardless. Perhaps more importantly, Munich is a base malt that is provided by many maltsters, while CaraMunich seems to be a Weyermann product.
As for the individual differences, I find that viewing the maltster's websites are a great way to learn about the qualities a malt is expected to impart on your beer. Using the Weyermann website for reference:
Munich (5.1 - 7°L)
Weyermann® Munich Type 1 malt ('Light Munich') is a kilned lager-style malt made from quality, two-row, German spring barley. Usually used a specialty malt, it has a high enzyme content despite its color, and can constitute up to 100% of the grist. It produces robust malt characteristics, including full body, amber color, and smooth mouthfeel. The flavor is strongly malty and the rich aroma has notes of light caramel, honey, and bread. Munich malt is typically used in dark lagers and ales, especially Munich-style lagers, various bock styles, and German festival beers like Märzenbier, Festbier, and Oktoberfest.
For the CaraMunich varieties, the description is basically the same across the board:
CaraMunich Type I (31 - 38°L)
CaraMunich Type II (42 - 49°L)
CaraMunich Type III (53 - 60.5°L)
Weyermann® CARAMUNICH® Type X is a drum-roasted caramel malt made from two-row, German barley. It contributes dark amber to copper hues, and adds a rich malt accent with notes of biscuit and an intense caramel aroma. CARAMUNICH® Type X also add body and improve head retention. Suitable for use in all lager and ale styles of beer.
The "malt aroma wheel" at the bottom of the pages seems to be the same for each as well. Given that, it's probably best to consider what the color of the malt tells us. Higher Lovibond ratings (°L) correspond to darker malts. So CaraMunich Type I will result in a light colored beer than Type III, assuming they're using in the same proportions. Similarly, darker colored caramel malts generally provide a deeper caramel or burnt-sugar flavor while lighter ones provide a more honey- or candy-like flavor.
All of that said, Munich is a base malt that can be used as a small or large part of the grist for different levels of effect. The CaraMunich malts are caramel malts and should be used in smaller quantities, as specialty malts. Ultimately substituting any of these malts for any another will result in a different beer. When a substitution is necessary, looking for a malt that is closer in color and description to the malt you a substituting would generally be better than using a malt simply because it has "Munich" in the name. Though it obviously depends on what you're looking for and in what ways you're willing to alter the recipe.
To maybe summarize a couple of the other answers here.
Yes they are different, and no they cannot be used in the same ways.
Munich 1 and 2 are kilned and are crystal malts, not base malts per se and can be used in mash or steep (in small quantiy). Similar to CaraMunich malts in flavor and color but do not aid body and head the way Cara malts do. Because the kilning is mild they can be 100% of the grist, but they have low diastatic power and will have almost no beta-amylase. But they still have starches to be converted, so are considered a "base malt".
All "Cara" malts have been malted and crystalized in a way to add body and head retention. Because of this they may be used in the mash or just steeped to get their benifiets. But the portion of the grist is a fraction of the base malts because they contain a lot of unfermentables. Using to much will make a beer sweet or even appear to have a stuck fermentation even though it's completely fermentened.
As far as color. All malts can be interchanged for a specific final SRM/lovibond. The underlying effects are flavor, aroma, body, head retention and residual sugar. So while color can easily be manipulated doing so effects the final beer in drastic ways. For example a 10% grist of SRM 20 crystal will have the same final SRM of a 5% grist of SRM 40 crystal malt. But the later will have less of the underlying properties and effects on the finished beer.