Slokas, Mantras and Stotrams

Mantra traditionally refers to Vedic mantras. They are only taught to those that have qualified themselves to learn them, and there are terms and conditions for their recitation. Almost always they are preceeded by a bij syllable, often Om.

Shloka can refer to any verse or even a section of prose.

Stotra and stuthi are prayers – often prayers of glorification. They may be written in prose or verse.

We can also add sutra to the list. A sutra is a code that expresses the essence of all knowledge in a minimum of words. It must be universally applicable and faultless in its linguistic presentation; this is the definition of sutra according to Vayu and Skanda Puranas. Thus we have Vedanta sutra.

On an interesting note, the Hare Krishna mahamantra is a Vedic mantra but it was originally chanted with Hare Rama Hare Rama first and then Hare Krishna second. I have heard that the order was reversed so that it was no longer a Vedic mantra and so anyone could chant it and there would be no hard and fast rules for chanting. This means that the power of Vedic mantras has been made available to everyone regardless of background, caste, creed, nationality or qualifications.

In some areas down south and up in Nepal it is chanted:

Om hare rama hare rama rama rama hare hare
hare krsna hare krsna krsna krsna hare hare

~Excerpts taken from a post by Murari Das

Another defenition:
A Sloka is referred to mean a verse of two lines, of sixteen syllables each, ie. written in the Anushtubh metre… An example of a Sloka would be:

Sarasvati namastubhyam varadē kāmarūpiṇi| Vidyārambham kariṣyāmi siddhirbhavatu mē sadā||

A Mantra, on the other hand, is a longer prayer, usually composed of many Slokas. It is also called Stotra… An example of a Mantra would be Shiva Tandava Stotra.