Is the word velhinho the same in Brazilian and European Portuguese?

No.

While the dictionary definition of "velhinho" (the diminutive of velho) is the same in both dialects, there are significant differences in typical usage and pronunciation.

In Brazilian Portuguese, "velhinho" is frequently used as a warm, common term of endearment for elderly people, even in semi-casual social interactions. It is often perceived as sweet or affectionate. In Continental Portuguese, while the word is understood, using it to refer to someone can sometimes be perceived as patronizing or overly "childish." Portuguese speakers are more likely to use "senhor" (to show respect) or "velhote" (to express a similar affectionate/informal sentiment without the infantile connotation).

Regarding pronunciation, Brazilian Portuguese tends to have more open, musical vowels and a more rhythmic, syllabic-timed flow. Continental Portuguese features more closed, reduced vowels and a stress-timed rhythm, often with much more prominent "sh" sounds (palatalization) in the consonants surrounding the "nh."

Brazilian Portuguese Examples

1. Meu avô é um velhinho muito fofo. (My grandfather is a very cute little old man.)
2. Aquele velhinho sempre me dá doces. (That little old man always gives me sweets.)
3. O meu cachorrinho já está velhinho. (My little dog is already old.)
4. Ele é um velhinho muito sábio. (He is a very wise little old man.)
5. Preciso cuidar do meu velhinho. (I need to take care of my dear old man.)

Continental Portuguese Examples

1. O meu avô é um velhote muito simpático. (My grandfather is a very nice old man.)
2. Aquele senhor está sempre a dar-me doces. (That gentleman is always giving me sweets.)
3. O meu cãozinho já está velhote. (My little dog is already old.)
4. Ele é um homem muito sábio. (He is a very wise man.)
5. Tenho de cuidar do meu avô. (I have to take care of my grandfather.)