You are correct.
A regular DVD-R or DVD+R is single layer. It can hold only (approximately) one-half of what a dual layer disc can hold. So, if you are dealing with an original source disc which used a dual layer disc, you simply have way too much data for your blank DVD-R or DVD+R.
And, most of the newer releases today are using dual layer discs when they are pressed at the factory. Not all, but a lot of them, especially the mainstream recent Hollywood releases.
When that is the case, your choices, then, are as follows:
-you can compress, and you will always lose quality, of course. How much depends on many factors (how much data is there; how much data was used for the main movie as opposed to extras; are there extra soundtracks like DTS; etc.) This compression means a quality loss in the picture. This is acceptable to some -- but then some people watch their DVDs on a tiny 13 inch screen, while others are using a ceiling-hung front CRT projector or LCD projector, and viewing the picture on a huge 106-inch screen. I prefer no loss of quality, which means no compression, so I choose one of the next options
-choice 2, you can use dual layer blanks for these backups. These discs will generally hold everything that was on the original, and you can make a "perfect" bit-for- bit backup. Your backup will be identical the original in every way, except it will have no copy protection and can usually be "Region Free." The downside is the cost of the blank media, which is still very exorbitant. It is getting better, but most are avoiding the $5 to $10 per disc.
-choice 3, you can "split" things and use two blank DVD-Rs or two DVD+Rs. This is my personal choice, but I am in the minority here. If you choise to split the material to 2 discs, you can then choose how to split it... whether you want to retain menus, for example -- if so, it will be a bit more time-consuming (and usually requires one extra piece of software).
-choice 4 is probably the most popular around here. It involves some combination or hybrid of choices 1, 2 and 3 above. For example, some people try to compress "just a little," and get the entire movie on one disc, so they do not have to swap in mid-movie. Then, they can store all of the extras on the second disc. In some cases, this technique can even be done using NO COMPRESSION for the main movie, and then using any required compression on the second disc, since it has only extras.
Dual layer discs were invented to allow more storage room on the disc. Obviously, if you decide to use single-layer discs, some compromise must be made, in some area. You must decide what is best for you. (Do you mind swapping discs in mid-movie? Do you mind paying very high costs for blank dual layer discs? Do you care at all about extras? How important are menus to you? How important is the time factor when you are backing up a disc? How important is picture quality to you now, and might this change with your next TV purchase?)