You've gotten some good input and explanations from others, but I'll add another way to look at it that may help. I'll try and give a clear breakdown that will help anyone who may stumble across this thread and be confused, or not have a complete understanding, so for the parts you already understand, just consider them a refresher on what you already know.
Radio Spectrum is divided into bands of frequencies and we typically follow the ITU definition:
https://en.wikipedia.org/wiki/Radio_spectrum#ITUFor amateur radio, the vast majority of activity is in the following 3:
HF: 3-30MHz
VHF: 30-300MHz
UHF: 300-3,000MHz
In amateur radio, we consider different parts of our authorized frequencies as bands and often refer to them by their wavelength. A whole other discussion could be had about wavelengths, but for now just consider that taking 300 divided by the frequency in MHz will give a good approximation of the wavelength in meters. There are many resources to find the amateur radio allocations, for example:
http://www.arrl.org/files/file/Regulatory/Band%20Chart/Band%20Chart%208_5%20X%2011%20Color.pdfFor illustration, some of the US amateur bands are:
40 meters: 7.000-7.300MHz
20 meters: 14.000-14.350MHz
10 meters: 28.000-29.700MHz
6 meters: 50.000-54.000MHz
2 meters: 144.000-148.000MHz
70 centimeters: 420.000-450.000MHz
In this case, the radio is a dual-band radio capable of operating in VHF and UHF frequency ranges. But the only covered US amateur bands are 2 meters and 70 centimeters.
Take a repeater with uplink/downlink frequencies that fall within the specified range, and all should be good....ALMOST!
The next item to consider is the mode that will be used on that frequency to transmit and receive information. Modes typically refer to the modulation type and operating protocols. In amateur radio, some of the commonly used modes are:
CW
AM
FM
SSB (USB/LSB)
P25
DSTAR
DMR
C4FM
SSTV
As a side note, there are some modes (FT8, APRS, PSK31, and others) that insert audio into the microphone input of a radio and use an analog mode such as SSB, AM, FM, etc to transmit the communication.
In this case, the radio is only capable of FM. Even if another radio were on the same frequency but transmitting in one of the other modes, communication would not be had. For example, this radio can tune to the frequency of a DSTAR only repeater in the 2 meter band but not communicate with it.
Now, some "digital enabled" repeaters for C4FM or DSTAR or DMR are in fact multi-mode repeaters that support both analog FM and whichever digital mode is enabled (as in the example K5LXP gave) while others are strictly digital or strictly analog. You will have to either experiment or get information from the repeater sponsor (information is often found on club websites) or another area ham.
Beyond this, there is one more step that gets added into the confusion as well.
After programming in the correct frequencies and verifying the correct mode, the next step would be to link multiple repeaters together as is often done. There are several ways to do this and many of the linking methods are independent of the mode selection. Historically, the main ways to link repeaters was via dedicated phone lines and RF links, now we also have internet based methods:
AllStar
EchoLink
IRLP
In this case, as long as the repeater uses FM as the mode on the RF side, it would be able to use whatever linking method the repeater has. However, if the repeater uses a different mode (such as DSTAR) on the RF side, the radio would not be able to use it whether it is linked or not and no matter what linking mode is used.
Hopefully this is a useful explanation that clears some things up, and perhaps will help someone else along the way as well.