All of these words have more than one meaning in a musical context, but I will attempt to focus on the meaning usually used by music software, since that seems to be what you're talking about. The best way to understand how terms like these are being used in your software is to read the manual, or at least look up the terms in the index.
You have loop correct, as far as I've seen. It's a bit of music that either can easily be made to repeated (as in Pro Tools or Logic) or is repeated by default unless you change the settings on it (as in Ableton Live or Fruity Loops). Most software can do MIDI or audio loops just as easily.
A groove in music software is a rhythm element that is extracted from a section of music. A groove is not music, it is musical metadata. The way you use a groove is for time alignment and quantization. Suppose you record a drummer and they lay down the perfect swing rhythm for the song. Then you try to record the bass player and they just can't get the timing right. So you tell your software to extract the groove from the drum part. It looks for drum transients and makes a note of when the drum hits occur. Then it can quantize the bass part to move the bass notes to the same time as the nearest drum hits. That is a way to quantize a part without quantizing it to a "boring" 16th note grid or something like that. You can do other things with grooves, and usually you can save grooves in a library and use them in other songs or for other things.
A pattern is usually an arbitrary part of a song that is built from a small number of measures that are all the same length and time signature. I agree that pattern implies MIDI data, not recorded audio. Patterns are mainly used by hardware sequencers and drum machines to make it possible to build up large songs while encouraging or enforcing reduced memory use (for a long time, memory for hardware sequencers was expensive). A pattern might be two measures of a drum beat that repeat four times for the verse of a song. Then there might be a different four bar pattern that repeats twice for the chorus. You can build up a song in the hardware sequencers by going into song programming mode and telling it to play the verse pattern four times, the chorus twice, then verse another four times, then chorus twice, then a bridge pattern, etc. This way you are encouraged to not program in every single hit of the verse, instead you repeat smaller sections and it saves memory. Some people also prefer to work this way.
I haven't seen section used in a device or software specific way. As far as I know, section just refers to "intro", "verse", "bridge", "chorus", etc.
Some other answers and comments seem to have muddied the waters, especially about the word groove. Yes the word groove can be used outside of music production hardware and software to mean something like the rhythmic feel of the music. But there is also a special definition used by several manufacturers to mean rhythmic metadata that can be used to adjust the rhythm of other elements. For example, the following is from the Beat Detective chapter of the Pro Tools Manual:
Beat Detective can extract groove templates, called DigiGrooves, from an audio or MIDI selection. DigiGrooves can be used to apply the groove, or feel of the captured passage to other audio selections (using Groove Conform) or MIDI data (using Groove Quantize).
The Ableton Live 9 Manual has an entire chapter on working with grooves, which starts (emphasis in the original):
The timing and “feel“ of each clip in your Set can be modified through the use of grooves. Live comes with a large selection of grooves, which appear as .agr files in the browser.
The easiest way to work with library grooves is to drag and drop them from the browser directly onto clips in your Set. This immediately applies the timing characteristics of the groove file to the clip.
Pattern is also easily confused with its normal definition. Here is an example of an explanation of what a pattern is in terms of a hardware sequencer, from the Moog Music Mother-32 Manual:
The Mother-32 contains a monophonic step sequencer. The Sequencer stores a list of single notes and expression information called a pattern that can be played back in a loop. As a pattern plays back, the Sequencer advances through each step and outputs a new note every time a step is reached. Each pattern can contain up to 32 Steps, and is easily stored in one of 64 available pattern locations. Patterns are arranged in 8 Banks of 8 patterns each.
Note that loop also appears in the Moog quote, which means in this case that once the pattern completes playing, it immediately starts again from the first step in the pattern. The Mother-32 does not have a song function where the user can chain together multiple patterns to form a song, but many sequencers do. The DSI Tempest drum machine has a song function, but in their manual they use the word beat instead of pattern to mean the basic set of steps in the smallest functional sequence element.