The Difference between Namo and Namah

Namo is just a sandhi form of namaH, the visarga H changing to o before a soft consonant. ‘NamaH’ before words beginning with k, kh, p, ph. ‘Namo’ before words beginning with g, j, d, y, r, l, v, h (namo gaNapataye, vaasudevaaya) H changes to s : namaste, etc. H is elided before a vowel: nama iishvaraaya. H changes to avagraha ( ~ S ) before a : namo.astu te.
Both 'namo' and 'namah' mean the same. There is a sutra in Panini's 'Ashtaadhyaayi' --- 'hashi cha'. It means that if the visarga is followed by words belonging to 'hash' group, then the visarga becomes 'u' and then to 'o'. The alphabets which are in 'hash' group are: ha,ya,va,ra,la, jna,ma, nga, Na,na,jha,bha,ja,ba,ga,Da,da,gha,Dha,dha. Examples: om namo bhagavate vaasudevaaya. Here 'namah' becomes 'namo' because the visarga is followed by the alphabet 'bha' and this belongs to 'hash' group. om namah shivaaya Here 'namah' does NOT become 'namo' as the visarga is followed by the alphabet 'sh' which does NOT belong to 'hash' group.