Tercero vs. tercer
The Spanish words 'tercero' and 'tercer' both translate to 'third' in English, but each word is used in specific grammatical contexts.
Tercero
'Tercero' is an ordinal number used to indicate position or ranking. It stands for 'third'.
Vivo en el piso tercero.
(I live on the third floor.)
Es el tercero en la lista de espera.
(He is the third on the waiting list.)
Tercer
'Tercer', another form of specifying 'third', is used before singular masculine nouns and it's also called apocopated form.
Es el tercer año que estudio español.
(It's the third year I've been studying Spanish.)
Este es mi tercer coche.
(This is my third car.)
Ese es su tercer intento.
(That is his third attempt.)
Summary
'Tercero' and 'tercer' both express the concept of 'third' in Spanish. The difference lies in their use: 'tercero', as a full form, is normally utilized independently or after a noun, whereas 'tercer' serves as an apocopated form being placed before singular masculine nouns.