There is overlap in terminology because different ingredients have multiple properties, it's not as simple as neat categories unfortunately. Plus there are industry definitions and lay definitions, and possibly slightly different terminology from country to country! You may also find different ingredients have different effects on skin and hair, so could slot into different categories .... argh!! Remember that skin is fed with water from the inside and potentially attracted from the outside, you can't really seal water out. With hair you could in theory seal water in, seal water out or attract water from the air.
The word 'moisturiser' seems to me to be the term used to have the most different meanings. Moisture = water not oil, if they are used interchangeably they are used incorrectly. A moisturiser is a skincare lotion or cream product (contains water, if it does not it is an ointment or anhydrous balm), you might also describe certain ingredients as moisturisers if they attract or increase water in the skin. From a UK perspective 'moisturiser' doesn't have a distinct meaning in haircare, the equivalent to a skin moisturiser product is a conditioner.
Oils and butters generally are occlusives or barrier agents, colloquially known as sealers. Lanolin and castor oil also have humectant properties but most oils and butters are not moisturiser ingredients in that they repel rather than attract water. However they can be a component of skin moisturiser products and of course haircare conditioners. Some lipids (fats) also have emollient properties, particularly in skincare because they may be able to attract water to the surface of the skin from the inside, in haircare coconut oil can increase elasticity which you could argue is an emollient property.
Fatty alcohols and cationic surfactants are classic emollients or softeners, these ingredients also have weak humectant properties which is partly how they soften the skin, they can also act as emulsifiers (mix oil with water) and so as gentle cleansers! They are classic ingredients in skincare moisturisers and haircare conditioners, if neither ingredient family is prevalent in the formula a product is likely not a conditioner or moisturiser.
The glycosaminglycans in aloe vera, honey, glycerin, hyaluronic acid, propylene glycol and proteins are all classic humectants they attract water fairly strongly (hygroscopic). Many humectants used in skin and hair products are carbohydrates but not all, there are some proteins and fats; table salt and epsom salts also have hygroscopic properties but would more act against hydration of hair than for. The humectant property is partly why too much protein can make hair feel like straw. Humectants are certainly moisturising ingredients, but aren't ideal to use alone, they are as likely to draw water out of the skin or hair as draw it in, they therefore work best balanced with emollients and./ or occlusives.
You don't need to be spot on with your terms but in the right ballpark is helpful, my big bugbear is describing ingredients that do not attract or increase water even repel water as moisturisers. Certainly oils and butters can seal in water if you applied to damp hair, you *might* colloquially describe the total act of wetting hair and then applying oil as 'moisturising'. But that does NOT make a plain oil or butter a moisturiser, if you apply an oil or butter to dry hair you have not 'moisturised' because water has not been added or increased.
If you applied a conditioner product to dry hair you *might* colloquially describe that act as 'moisturising', since you are adding the water found within the product and the ingredients might be able to attract more water from the air. It is my bugbear because it's clear some people end up thinking they can condition or moisturise with occlusives alone, they then miss out on all the benefits of the classic humectants and emollients.
Someone else may well give you different answers tho!
2a-2c, medium texture, porous/ colour treated. Three years CG, growing out mechanical and chemical damage = breakage and very high porosity. Past armpit length heading for waist.
Treatments: Komaza protein, Komaza Matani, coconut oil with sugar syrup. Hairveda Sitrinillah
Leave in: Fructis Sleek & Shine (old), Gliss ultimate volume
Styler: Umberto Giannini jelly, Boots curl creme, Rockin RInglets
Experimenting with: Mega-Tek, Curl Harmony reviver, Elvive Full Restore 5.