ESL= English as a Second Language, this is the name of the subject, this is what we call English language classes in English-speaking countries, students are living in these countries as students or immigrants and are often multi-lingual
EFL= English as a Foreign Language, another name for the subject, this time for classes in non-English-speaking countries, students are generally trying to learn English for a variety of reasons (work, school, hoping to emigrate to or attend school in an English-speaking country, etc) and are usually mono-lingual
ELL= English Language Learner, this is the name of the student
ESOL= English for Speakers of Other Languages, often shortened to ESL, this term came about because for many people English is their 3rd, 4th, 5th....language, rather than their second
TESOL= Teaching English to Speakers of Other Languages, this is the name of what I do and the official name of most degrees in the field
L1= first language, this would be referring to a person's native language
Low Intermediate= this is a student who is still is the beginning stages of language acquisition, but has the general structure and a good amount of basic vocabulary, there is a wide range of proficiency levels included in this term and it's generally a good idea to follow up such labels with more questions to get specific details on what the user considers LI to be
High Intermediate= this is a student that is progressing well in their language, it is likely that they can use the language quite fluently in daily situations and accomplish everything they need to socially, they are still lacking finer grammar points as well as academic proficiency, it is also not unusual for a high intermediate student who speaks English at school but not home to be lacking in basic vocabulary for home items and activities; again, this is a broad label and needs some clarification based on who is using it
Native-Like Proficiency= often shortened to just Proficient, this describes a learner who is able to use the language with great skill and in every situation, to the trained ear there will be indications that English is not their first language (unless he/she started learning English at a very young age) but the general public may not realize it and will have no trouble understanding and communicating with this person
SIOP= Sheltered Instruction Observation Protocol, this is a method of instruction that has been researched and proven to work well with ELLs, but don't put it aside due to a lack of ESL students, it's also very effective with special education and intervention students
IELTS= International English Language Testing System, a standardized test for non-native speakers of English who would like to study in an English-speaking country (more utilized in Britain)
TOFEL= Test of English as a Foreign Language, a standardized test for non-native speakers of English who would like to study in an English-speaking country (more utilized in the USA)
This list is far from exhaustive, but these are the terms you are most likely to encounter in the general education world. I hope it makes things a little bit clearer, but if you are still confused feel free to ask! ESL people are teachers and we are very experienced at explaining what words mean; it's kind of what we do. ;)